@Rosemary They aren’t, no. They’re a different classification altogether, while being rare(ish) on trainers because of the story of Sun/Moon.

I haven’t tested to see if that rarity applies to the postgame of USUM though, so they may still be on trainers.

@Goldkin Also, what prompted this in the first place was learning that apparently no trainer in gen 2 had a skarmory, which might be why we thought skarmory was a gen 3 pokemon for the longest time.

@Rosemary Gotcha. Many ultra beasts in regular Sun/Moon definitely qualify then, though they’re less likely to be “missable” since they appear as wild Pokemon in story.

I can’t think of any other immediate examples of not being introduced through trainers in the game the Pokemon first appears in. Though I’m thinking some of the dream Pokemon from B2W2 likely also qualify (I never played through or tried those).

@Goldkin I don't think any pokemon are exclusive to the dream world.

@Rosemary Yeah, double checking the posted lists, it seems like there were indeed no exclusives introduced in that game: https://www.smogon.com/forums/threads/list-of-released-dream-world-pokemon-and-attacks.80928/

@Rosemary I don’t see a conclusive way to check, but it seems Serebii lists known trainers for all Pokemon.

It seems they don’t separate original GS from HGSS however:
https://www.serebii.net/pokedex-dp/trainers/227.shtml

@Goldkin I'm more inclined to think that they just don't have trainer data for gen 2 games, since that's specifically on their gen 4 pokedex.

@Rosemary Yeah. And it looks like veekun’s location database is currently not up, so maybe someone needs to scrape the older game data again.

@Goldkin It wouldn't be hard now that we have the disassemblies.

@Goldkin None of the trainers who have skarmory in gen 4 exist in gen 2, anyway. Well, Jasmine does, but you only battle her in Olivine, never in Saffron.