What if abilities were split into “traits” and “skills,” where “traits” are permanently stapled onto the species due to it being inherent to their physiology (stuff like levitate, iron barbs, liquid ooze, etc.) and “skills” being ones they have to learn and are limited so if they want another skill, they have to replace the old one? (stuff like technician, super luck, moxie, inner focus, etc.)

Seems legit.  It’s sightly awkward in that you wind up creating this major gameplay distinction between learned and inherent abilities that is based entirely on aesthetics (like, as far as I can tell there is no mechanical criterion that separates the two groups you’ve outlined).  Maybe at some point the developers actually want to have a Pokémon that can get Levitate but doesn’t have it automatically (the way Bronzong is now)?  Of course, you could just rule that things which are inherent “traits” for some Pokémon can be learned “skills” for others.  You also need a mechanism for learning skills (but that could be as simple as having them be learned on level-up like moves).