Well, that statement was actually referring to the sixth generation’s treatment of older Pokémon in general – which you can contrast sharply with Black and White’s (unprecedented) total exclusion of them – more so than to cries in particular, but since you bring it up… no, it’s not “the most distinguishing trait of a Pokémon;” I’d actually go so far as to call that a truly ridiculous assertion. I mean, if you look at Vileplume and Aerodactyl, the difference between their cries, originally, was all but imperceptible, despite their being totally different in every other respect. Likewise Ditto and Poliwag, Charizard and Rhyhorn, etc. And then there’s the fact that, while most of a Pokémon’s characteristics are constant across different media (games vs anime), the cry is rarely even similar. I saw it as an example of Game Freak paying attention to older Pokémon and giving them something to help ensure that they would feel every bit as shiny and polished as the new ones. Perhaps nostalgia is the wrong word for that, but I still feel my original sentiment is justified.
