I get the idea. You love someone, and you want them to be happy! But there's one part that bothers me... see, I've noticed a lot of people in the Troper Tales talking about how 'even though it broke my heart, I didn't tell her/him, because I wanted to be happy.' That part bugs me, because that's wrong. Morally. If you love someone, you should tell them. You shouldn't try to take them away from the one they love, but it's selfish not to even tell them. They have a right to know. I have a girlfriend, but if one of my friends cared for me that way, I'd want to know, and I'd be upset that they hadn't told me if I found out, just because they should have. In addition to that... what's so noble about repressing your emotions that way? The tendency to help them in any way you can, even if it means helping the relationship that is getting in your way, is one of the things that makes me think humanity might pull through, but shouldn't you at least put your cards on the table? They might even care about you the same way... simply not telling them just... isn't right for anyone. If the one I loved was in love with someone else, I'd go barefoot over barbed wire before I tried to come between her and the one she cared about, but I'd let her know, and if she didn't feel comfortable maintaining the friendship, then I'd accept that. I think that's what is intended by "I want my beloved to be happy." Accepting their choices, rather than precluding them.
Sometimes, it would cause a lot more trouble than it solves. Your beloved might be married to someone they love very much, and a confession would only cause disruption to their marriage. Alternately, someone who is bisexual or gay could harbor a crush on their straight friend, and know Incompatible Orientation is in play. You could also still harbor a torch for an ex that you know, in your heart, wasn't meant to be and letting them go is the only way to keep your sanity.
The "put your cards on the table" part assumes that someone who follows this trope necessarily hasn't tried another way first. Not necessarily the case. After one year of a relationship with someone, you can realize that it's time to let it go. That you were only a step on Alice's way to Bob, and that the care you have put in helping her improve her self-esteem and will has only given her the strength to fly away from you, and go with the one she wanted to begin with. In this situation, you feel betrayed and badly mentally broken, and helping those two people to get together is both a way to get this over quicker and put some emergency tape on your self-esteem in an "after all, I'm still a nice and lovable guy in my view" way.
The part that bothers me about that argument is the "they have a right to know" bit. It's your emotions, not theirs. If you want to tell them you love them, go ahead, but you have every right not to tell them. It's a deeply personal choice deciding to tell someone how you feel about them, and I have a hard time to see how it's morally wrong not to. These situations do not lend them to a black and white decision making process. (And generally, unless you're deliberately and knowingly wrecking their love life, there isn't a morally wrong choice either.) It's not selfish to not tell someone you love them romantically. Plus, this trope seems to come into play mostly when there's another compatible lover for the person in the picture, or just some bigger goal that you might hold them back from. Also it generally appears in these scenarios that the choice has already been made on some level; it's about letting go of something as an expression of love.
Is it necessarily the 'love' that they weren't telling about, or was it perhaps the 'broken heart'? If you want the other person to be happy, well, ignorance is bliss. Personally, I would want to know if my choices were breaking somebody's heart, but the knowledge would make me miserable.
I still don't get the flip-side of this trope, which is that the "beloved" might only be thinking of themselves. There's no honor in that. Assuming that whoever is being left is truly an alright person, couldn't the leaver find a lover for the loser? I mean, wouldn't that create a bit more happiness? I admit this happened to me, twice, but I only acquired this viewpoint from the second time due to the way I was treated by this otherwise lovely person. The first time I only had a desire to let them be happy, the second time I felt... taken advantage of. I snapped myself out of it for feeling "immature", but, like most immature people, I felt like I didn't have to be nice to them if they weren't nice to me. And then I slapped myself because that's like trying to fit a square peg in the round whole of my character. I had, and still have, great respect for the two I'm no longer with, and I've moved on, but I just haven't found an answer to this... ethical dilemma.
In those cases where the beloved is thinking selfishly, it says more about the honor of the one giving them up that they allow them to make their own choices, rather than holding them to a moral code that would make them unhappy. Nobody said the beloved had to be honorable. Also, who would really be happy to be set up with somebody else by the person they want to be with? I wouldn't, and I wouldn't want to be the "consolation prize" for somebody else, either.