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Legendaries are not necessarily one-of-a-kind. Especially ones like Articuno/Zapdos/Moltres, which have absolutely no reason to be unique. It probably wouldn't be much of a stretch to say that most legendaries are simply ultra-rare species that humans have made up legends about, rather than some sort of lame "ZOMG THE POKEMON GAWDZ" thing.

And Latios/Latias are quite obviously just the male and female of a species, just like how the male/female Nidorans are. The Pokédex entry for one of them even says that they live in COLONIES somewhere... which means there has to be more than one of each. So "more than one Latios" isn't one of the anime's mistakes--it's one of the few things they got right.

Of course, there are some exceptions (multiple Mewtwos wouldn't really work, since there's very little chance of someone duplicating the experiments that made the first one after the Cinnabar Island lab got blown up), but for the most part, the only reason legendaries are one-per-game is to make them seem ultra-rare compared to regular wild Pokémon--a "you probably won't be lucky enough to see more than one in your lifetime" type of thing, rather than "there's only one in the world."