Ratskinner
Adventurer
In Apocalypse World going aggro is based on Hard, while acting under fire is based on Cool.
Are you envisaging a long list of movews each associated with a particular stat - or are you envisaging changing the state to reflect genres and what is expected to matter in play? The former seems like it might still be genre-limited. The latter seems like we're now setting out a whole design philosphy or approach rather than an actual system. (I would put PbtA - as opposed to any particular PbtA game - in this category.)
This looks like you're describing a meta-system - a basic system structure/framework, with the details to be cashed out based on particular genre.
Either, I was just citing it as an example/extension of what I was talking about. I think for a "universal" version of something like this. I would include only a small set of general action types (as Fate does). For the sake of designer sanity, I would personally not want to write a genre-spanning set of specific moves. I generally agree with your assessment, although I think there's a bit of a gray area between system and meta-system for games like Fate, Strike!, or even Savage Worlds, that provide a relatively strict design framework with flexible trappings attached. PbtA doesn't (AFAIK) have such a "core" as part of its zeitgeist is tying all the mechanics very closely to the material thematically (even if its core is fairly easy to suss out).
I think that there is a relationship between system/mechanics, and the sort of thematic "heaviness"/"seriousness" that a system can produce/support.
I tend to agree, although I see the "heaviness"/"seriousness" dimension as something rather easily tweaked. (perhaps depending on your core mechanics). IME, things like investigative vs heroic action are much more problematic. I think the introductory material in some of the earlier Gumshoe games was pretty spot on about how there are fundamental differences in the nature of designing a scenario.
I'm asserting that neither Prince Valiant nor MHRP can handle really serious genre/theme - eg WWI - because of their approach to consequences. Whereas I think BW and AW can handle more serious stuff.
I'm not sure it's easy to explain why, but here's one thought: in Prince Valiant it is always up to the GM to stipulate the consequences of being dropped to zero in Brawn or Presence as a result of conflict. How would the GM, in good faith, stipulate a consequence of (say) drowining in chlorine gas in a shellhole? In MHRP a player has to stipulate a consequence (a complication, or pushing through Stress to Trauma), to bring it about.
Whereas BW puts it much more into the system to produce harsh consequences. And makes it easier for players to put more on the line in their action declarations.
IME, this is definitely tied to player buy-in. I mean, if I sign up to play in a WWI game I've got to think that's a possibility. If nobody at the table wants to hear or say those things...then why are we playing a serious WWI game? I'm not sure why its any better that the GM say...reads the gas results off of a chart rather than describe them ex tempore.
However, there is definitely a mechanical influence on these things, but I've seen it go a couple of ways. In looser games, once the "improv" juices start flowing....things tend to get progressively sillier. Just human nature with a bunch of clever people, AFAICT. Then again, my experiences tend to go the opposite direction from your example. i.e. A GM is shooting for a grimmer/more serious game, but can't make it happen because...mechanics (I won't mention HP here, I just won't....darn it.)
To cross this back to the previous issue, I thought the recovery/Vice mechanics in Blades in the Dark were/are pretty genius. Without writing an encyclopedic list of such optional subsystems, I don't see a universal system of any kind is to be designed that fits all genre possibilities.. However, with the stipulation that this would be some kind of "standard" heroic rpg, I think I would still lean towards using a "dramatic" framework for the attributes.