Where is it that these games fall apart - the story or game mechanics? I've heard a lot of mixed stuff about City and Knight, while Asylum and Origins seem to be pretty well-loved.
Story, for sure, with the main three Rocksteady games. Asylum is fine, though it falls into cliche video game tropes of villains getting more powers because reasons, but the overall story is a simple and straightforward one with solid characterizations and solid writing that captured the characters well with a few key exceptions such as Bane.
City started fine, but became a mess about half way through by shoving in way, way too many villains while discarding a very interesting one they had been building with Hugo Strange, and then discarding all of the other villains they didn't need to be there to begin with just to focus on another Joker/Batman lovefest that we've seen a thousand times in one way or another for a shock ending that was, honestly, kind of dumb and pointless even if it made you go, "Wow, they went there. How about that?"
Knight is just kind of a mess from the beginning. A lot of stuff going on, much of which just isn't built up well at all, such as the Arkham Knight himself, whose storyline and arc is so mishandled it basically makes no sense anyway, Joker needlessly just in for...reasons? And a plot that kind of, sort of makes sense, but really doesn't so much, and it obviously more of a reason just to have another empty open world city than anything else. Stuff with Scarecrow is pretty solid, though, so there is that.