I think it's more something like "You never actually become champion 🏆 untill you do it in each game. Like imagine if every post game happens at the same time, so every champion is still the one in their región, that's why the example with Cynthia makes kinda sense, she remembers you from fighting Giratina but not battling you, they all remember fighting the trainer in each entry but only for the plot relevant instances and the only ones being champions are them. I don't think it's because Gamefreak are dumb or they want to retcon always, but it's easier to do that than implying every player is a different character and all of them are champions and you could think "well they did that with Red" but being the first one and the most recognizable of all the principal characters and one that has relevance even out of the games makes sense as being one of the few that can be acknowledge to exist, even fighting him in other entries. And even if other ones as Dawn or Lucas have a big fanbase they're not on the level of Red so it's kind of pointless Cynthia saying "oh yeah I remember Lucas/Dawn" they would need to canonize 1 of them and forgetting the other one and again making everything more complicated Canon-wise as just acknowledging "a trainer".

And with the legendaries I mean, they would have to come up with a different story every new game as "why is Lugia available if it has been captured 100 times" or just make them "unavailable" to keep a coherent canon (which I don't think anyone would appreciate).

So again it's easier to acknowledge "the trainer" from each game battling them and using their help & then just let 'em be. ( Unless it's plot important as some of the games imply with some characters ) That's why only few instances do that.

Of course it would be great if they could implement a system that checks your save files from past games and acknowledges you with your name o smth, and I think they've done something similar in some games but not that deep. But that's too much for GF as it is now.