The reason why Travis didn't have his revelation until right after the second rank boss fight is because all of the other assassins he faced were either weird (Margaret), demented (Matt Helms) or non-talkative (Ryuji) enough to not think of them as anything more than obstacles on his way to get revenge (and even then Travis showed some amount of sympathy towards Ryuji and Margaret). It wasn't until someone semi-normal actually talked to Travis about how insane everything had become to make him realize how wrong the ranking fights are. Plus he was right next to getting his revenge so he'd be thinking more clearly by then.
Besides which, all of his opponents up to that point, sympathetic or not, all seemed to still enjoy the fight; Margaret was a Graceful Loser, sure, but she also spent the whole fight talking smack to Travis through her song's lyics; Ryuji was a Worthy Opponent who seemed to enjoy the fight just as much as Travis, and even Captain Vladimir, who Travis arguably showed the most sympathy for after defeating until Alice, mistook Travis for an alien and forced Travis to kill him. Simply put, while Travis was starting to have his doubts before, meeting Alice, the only person in the competition who seems to truly hate being a part of it, made it all hit home.
Also, why Travis wears all of his katanas on his belt, instead of leaving them under his bed like in the first game. As well as being more convenient to the player, it's to prevent a situation like in the end of the first game, where he's caught unaware and unarmed.
Bizarre Jelly gets expanded from three to five members. Bizzare Jelly 5. BJ 5. B Js. Blowjobs.
Instead of a cool, suave, Magnificent Bastard we get a little shit with no fighting ability outside his little toys for a Big Bad. This is to avert Do Not Do This Cool Thing, because the theme of the game was how petty and stupid revenge is and the morale would be lost if they had made him charismatic in comparison to Travis or indeed, fullfilling to kill at all.