I have multiple disparate thoughts going on here...
1. Tournaments aren't like Battlegates. You fight multiple battles in a row, often including characters from that world, FF characters, and recurring Disney villains (Pete) as opponents. Battlegates are one-off battles, primarily against Heartless. Battlegates don't compensate for that the tournament side quest's absence, imo.
2. I enjoy Battlegates even though I think (and wish) they could co-exist with a tournament mini-game in the same game.
3. I want Olympus to return someday, even if it takes a break for a couple of games. There are still a lot of things they can do with that world, imo; it's one of the few that could go on forever, tbh.
4. At the same time, a tournament mini-game *doesn't* have to reside simply within a Hercules world. As mentioned, they did it with Mirage Arena. But they could also do it with worlds like Robin Hood (the tournament where Robin Hood competes for Marian's hand), The Sword in the Stone (there's jousting in that film, and a whole brains v. brawn theme), etc. All it would take is some creativity to create a new tournament side game somewhere else. I mean, I could picture one in the Mulan world where you fight all the different characters amidst Heartless (Shang, Mulan, the three soldier friends) or maybe some kind of sleazy competition in the underworld area of The Great Mouse Detective or perhaps a tournament in the Realm of Monsters in Moana (and you could fight Tamatoa, the little coconut creatures, and Maui amidst Heartless). The coliseum in KH1 was an original idea itself based around the fact that Hercules features a lot of fighting in that film. You can do something similar with another film without it being a verbatim copy. It's just like how the musical minigame in KH2 could be done with so many worlds / films.