@Rosemary MissingNo.

As for numbered Pokemon, the games usually ensure full coverage (if not main game, in postgame and Battle Tests, etc). Newer Ultra Beasts, for example, may qualify.

@Goldkin Are ultra beasts not legendary?

@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/