The Dragon Lord
Given the way Pokémon games are set up, it's probably safe to assume that the reason you can catch the same Legendary in multiple games isn't as much about the fact that there are multiple of that Legendary, but more because the first one was never caught in the first place. By that, I mean to say that the capturing of a Legendary in any given game is to be considered a non-canon event to future games, which take place in an alternate timeline where the Legendary wasn't captured. For example, it's probably safe to assume that there's only one Palkia, seeing as it's a literal god, (maybe two, if you want to count the Arceus event in Heart Gold/Soul Silver, but that's the maximum) and yet we can capture Palkia in Pearl/Platinum, Omega Ruby, and Ultra Moon. Obviously there's not three Palkia running about. The way to resolve this is to have it so that in the continuity of Omega Ruby and Ultra Moon, the player character from Pearl/Platinum never captured Palkia in the first place. The events of the game may have occurred, but the character chose not to capture the Pokémon.Then you have the fact that the same legendary can be obtained in multiple games, which is true of most legendaries.
If you want a more practical example, Red, in canon events, probably never caught Mewtwo (or any other Legendary, for that matter), or else he would likely use it against you in (Heart) Gold/(Soul) Silver and (Ultra) Sun/Moon, despite the fact that nearly anyone playing as Red most likely did capture Mewtwo.