This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
Trent is right and Bink's talent has been arranging everything.
Trent theorized that the escapades Bink was involved in were actually to arrange better security for him. This appears to be right. After all, by the time they're over, Bink isn't just in a high ranking position-no, he has an entire dynasty of Magician-Kings to protect him from any harm that may have come his way. And any new Magician or potentially dangerous person entering Xanth was quickly married off to a friendly character to keep them pacified. Given the fact that his talent can make small causes lead to large effects and that many Xanthly adventures relied on a small coincidence, it's possible that his talent is what led to all the Demon bets being won, and even in XANTH himself falling in love and getting tied down to help the inhabitants of the land.
Also, Bink's talent protects him from everything, not just magic. While Trent could harm him with a sword, he didn't kill him, and events have conspired to not have him killed by mermen, drowning, falls, etc.
Naturally, that's because there is nothing in Xanth that isn't affected by magic at one point or another.
The two cases of Bink being harmed in Xanth (Trent's sword and getting injured, possibly permanently losing a finger because of an ordinary knife as a child) both involved non-magical objects. However, in the fourth book, despite going to Mundania he is rescued due to a whole bunch of things coming together, including his own magician son. It's possible that rather than magic not being able to harm him, his talent manipulates magic to protect him, which explains why it would cause him to develop a Badass Normal skill set. Or, his talent might be trying to protect him from everything, but it has to manipulate magic in the things around it in order to do so. Mundane weapons won't have any internal magic, and thus his talent wouldn't be able to prevent him from being injured by them, aside from making sure that he knows how to fight and so on.
Bink's talent is that he doesn't have a talent. He just has amplified Plot Armor because he was the protagonist of the first book.
Incorrect: his talent is almost an outright character in the second book. Not to mention that if he didn't have a talent, nothing would have happened when the demon X(A/N)th reversed it. However, his talent could be described as a Deconstruction of Plot Armor. For instance, while it does ensure that nothing permanent happens to him, by refusing to reveal itself and so on it ensured that he experienced a lot of plot requiring that armor.
Bink's talent is sentient and essentially a split personality. This was caused by the talent itself.
The fact it is clearly capable of planning ahead for scenerios in the books clearly demonstrates that it possesses sapience (the ability to think and plan): self-awareness is a prerequisite for that.
The closest equivalent to his talent in Xanth's history is Magician Murphey's. He possessed the ability to make things go wrong for the person or thing he cursed, while Bink possesses the ability to make things go right for himself. Murphey ended up suffering from the collateral damage he caused, and without that second personality, Bink likely would have had the same fate.
The very nature of his talent involves and requires viewing everything magical around him, including his own family and loved ones, as chess pieces that can (and in fact must, given the rules of his magic) be manipulted or even sacrificed if that's what it takes to preserve his own life. He was saved from inhaling poison gas as a child because his parents were in position to do so with a very narrow window, and his talent was willing to let Chameleon die, using her as a living shield against Trent's mundane sword.
Xanth in the early books is a Death World. Growing up aware of his talent would have caused him to think that it was necessary and therefore ok to be a Manipulative Bastard. His talent does act for the benefit of those around them, but only as their well-being affects his own (for instance, letting his parents get killed would mean they wouldn't be around to use their talents to save him from more poison gas, and his descendants having magician-level talents and loving him is also a huge advantage).
Now, in a different series, this would be fine, and Xanth does toy with grey and grey morality in the first couple books. However, Anthony is on record saying that Lawful Stupid is the ideal, and the Magnificent Bastard characters in the Xanth series (Trent, Murphey, the Dastard) regularily suffer because of some consequence of their selfish actions. Anthony uses Grundy the Golem to Show Their Work in a scene where he demonstrates game theory and why cooperation with trust is the best strategy for long-term victory in a later book (the ninth?).
An example of this is the Bink vs. Trent battle in the first book. At that point, Trent did have the capability to kill him, and after witnessing Bink's talent's biggest Kick the Dog moment (being willing to sacrifice the woman he loved to save his own skin) and, if it weren't for the fact that Bink was his friend and a fundamentally decent person, would have done so. At this point, the practical thing would have been to kill Bink, as Iris pointed out. He's the one person capable of keeping Trent from the throne, his talent is unspeakably dangerous and Trent knew it, and yet Trent couldn't do it. Due to the Power of Friendship. Since Evil Cannot Comprehend Good, a Bink who had grown up manipulting others would not have been able to use that power, and would have died then and there.
The climax of the second book is another example of why having a second personality that's unaware of his talent is to Bink's advantage. He is able to win over the Demon X(A/N)th, a member of a race who spends all their time trying to out-swindle each other. He is also, due to the Badass Normal skill set not knowing about his talent forced him to develop to survive in a Death World, able to keep himself alive when the demon reverses his talent to see what will happen. If Bink's only skill had been using his talent to protect himself, his weapon being turned against him would have killed him.
Bink not being aware of his talent has demonstratably helped him protect himself. Creating a surface personality unaware of his talent allows Bink to simultaneously have all the advantages of a Lawful StupidBadass Normal with the Power of Friendship and a Magnificent BastardChessmaster (very skilled at Xanatos Speed Chess) with a total willingness to Kick the Dog if that's what it takes. That's practically a Ying Yang Bomb, and the first four books do a very good job of showing how there's really not much that it can't handle (and what happens to a Xanth that doesn't have that talent). Murphey is in many ways the anti-Bink, and the third novel doesn't go well for him or anyone else.
People aren't allowed to know about Bink's talent not because of some additional part of the magic, but just because Bink's talent includes itself.
In other words, Bink's talent isn't 'magic can't harm him', but 'he can't be harmed if the cause included magic at any point'. The book explicitly points out that if people knew about Bink's talent, they'd hurt him other ways, so his talent hides. However, what's not pointed out is that they'd choose to hurt Bink that way because of his magical talent, and that would be magic, i.e., his own talent, causing harm to Bink. We don't need to postulate some extra ability, or his talent being 'smart enough' to hide, it's simply that 'doing something non-magically harmful to Bink because a magic talent exists' counts as 'being harmed by magic'. The magic itself doesn't have to be the harm-inflicter, just a link in the causal chain.
Which means that if people knowing other information about magic would be eventually be harmful to Bink, no one could learn that either. And nothing that, however indirectly, is caused by some magic existing (Which basically is all of Xanth) can ever threaten Bink's life.
Which raises a lot of interesting questions about the Demon XaNTH and his recent behavior. The assumption seems to be that because Earth taking over, or whatever the current bet is, would cause the magic to go away first, and then whatever bad to happen, this would be allowed by Bink's talent. But if XaNTH counts as 'magic', then, by definition, he cannot lose these contests he keeps having, or 'magic' would have harmed Bink. Does XanTH know this? Is he essentially cheating? (Of course, his talent has no problem with magic going away temporarily if it results in him being better off at the end, so could rig the contest the other way if it knew it'd eventually be okay.)
Panties DON'T knock men out
The seeming ability of panties to turn men into drooling morons is a carefully constructed facade by the men of Xanth to get women to stop wearing them. Day to day life tends to get Xanth women near-naked all the time, so why not go for the whole fun view?
Magician Humphrey rules all of Xanth
He's just smart enough to let the kings think they do the work.
Or he's smart enought to actually let the kings do all the work while he has sex with his wives. His book demonstrates pretty clearly that he doesn't want to rule Xanth, he prefers do work on the stuff he cares about and keeps getting forced to abandon his own work temporarily when things get messes up or there's no potential king. His question system seems designed to enable other people to do quests and ensure stability so he doesn't have to.
Ted and Monica will destroy the Adult Conspiracy
Xanth had its share of mischievous kids, but let's face it, those two really take the cake. (And eat half of it before dinner while hitting you in the face with the other half, but that's another story). While some people under the ordinary age of induction have discovered the secret of the Conspiracy before, they all immediately switched over to the side of protecting kids from harmful information. The only ones mischievous enough to betray something of this proportion are demons, and they think it's more fun to maintain it to annoy all the kids. But if Ted and Monica ever find out the secret, they'll tell it far and wide, delighting in the undoing of such a grand project. And they're already pretty close to knowing, anyway. All it would take is one lucky guess...
Love Springs are leaking into the atmosphere
There seems to be more love springs out in Xanth than any other type of magic spring. And as we all know from studying the water cycle, water evaporates. So the atmosphere in Xanth is bound to have trace amounts of love magic in it, explaining why everyone's so keen to pair up.
Reverse Wood is responsible for absolutely everything, ever
Reverse wood reverses the effect of all magic. But reverse wood is magic itself. So surely it would reverse its own magic, making it ordinary wood (inasmuch as anything in Xanth is ordinary). But if it was ordinary wood then it wouldn't magically reverse itself ... so not only is it in a dual state of magic and non-magic, it also controls the magic of everything around it, dictating what is and is not.
Reverse wood does have limits; it was overloaded by all the curse fiends working together— individual curses are converted to blessings, but load on too many of them and it's splinter time. So it's likely reverse-wood has other limitations, such as immunity to its own effects.
In the first book, there are anti-magic plants that evolved on the edges of Xanth's magic field. Since magical plants had advantages over mundane ones, those plants evolved to nullify the abilities of their competitiors. Trent weaponizes this. It's likely that reverse wood is the same idea writ large: an adaptation to enable survival in an area of insanely high magic.