And can innate ability be improved, or is it a static thing? I'd argue the former. Intelligence can be defined as one's skill at learning mental skills, and I know from personal experience that the more I've learned the easier it's become to learn new things. Similarly athleticism could be defines as the ability to learn new physical skills, and again from personal experience, as I've engaged in weight training, it's become easier to learn all other physical skills. One could argue that this is a cross-skill benefit or synergy rather than innate ability, but I would see this as a bit of a semantic argument. For an RPG, after doing game designs with skill synergy and designs with skills increasing attributes, I'd days the latter is superior as it's easier to implement and can be used to achieve almost identical results.
I think of ability scores as a combination of innate talent plus what the character developed as a child. All the things a person practices early will develop their innate talent (whatever that is) the most, fastest, easiest. That's why a character can get to 12 or 15 or 17 by the time they start going on that first adventure. Then it gets more difficult to improve. The way it is modeled in most games may not be all that realistic but the general slowdown corresponds roughly to the way it happens in real life.
The model is always going to have holes because of how complex most skills are and what abilities they draw from in what proportion. You can have, for example, the best raw Dexterity imaginable, but if your depth perception sucks, you aren't going to show as a "+3" or "+4" to hit with a bow once you get the entry-level training, and just to stay in the ballpark with another person not suffering under the detriment is going to take an insane amount of practice.
Arguably, people with "High Dex" should learn "Dex-based" skills faster, too, because of their brain already having spent a lot of early time on getting good at such things. I guess that's the basis for the early D&D bonus to experience for a high characteristic. I'm not sure I like that from a game play perspective.