For a different system, perhaps. Not for D&D. At one time I did want such a thing. I have decided it is too controversial and unlikely to be effective at the goals it would need to meet.
Skill Challenges are a decent start. They aren't quite enough, but they're the foundation of something really quite good if we continue iterating on the design.
Allow me to give a combat specific example of what I mean, since those rules already exist. Imagine you have two classes, Warrior and Dervish. Warriors and Dervishes generally do the same kinds of things (hitting stuff with weapons, surviving hits from enemies, etc.), and they make the same number of attacks per round. In Playtest Q, Warriors get +1d6 bonus damage on each hit, while Dervishes get +4 damage per attack, hit or miss. Prior to Playtest Q, their damage output was essentially equivalent. Clearly, in this context, the calculation indicates Dervish is just better than Warrior. There is no comparison; +4 guaranteed damage on every attack, hit or miss, is clearly superior to +3.5 average damage only when hitting. This is not interesting gameplay. It is a dull, rote mechanical calculation.
We can do similar things with other stuff, even real actual rules. Like 3.X's Full Attack action for "martial" characters. Quantitatively, there is no contest, you should always Full Attack if you're able as a Fighter or Barbarian etc. Nothing else even comes close. But this produces incredibly dull, static fights where people just stand there whaling on each other. The Spheres of Might rules supplement for Pathfinder 1e addresses these issues by creating Special Attack Actions (SAA), which cannot be used in a Full Attack, but which can—note the word "can"!—be good enough that you'd choose not to Full Attack. This was very intentional design; the Spheres of Might rules actually make combats both more dynamic (because people can move around, so they should!), and more tactically engaging, because now you can have two or more different SAAs, alongside the old reliable Full Attack.
Now, as noted, I don't want "social combat," so the specific details here are not relevant, only the overall thrust of having options that must be weighed against one another for what they are and how they work, not their brute numeric size. The nature of "DM says" inherently runs counter to this, because it is DMs approving or disapproving of player proposals, rather than the players trying to solve the metaphorical "puzzle" before them with understood, usable tools. At best, "DM says" is about convincing the DM to let you use your biggest bonus every time (a complaint people really do make even about 5e!)
A system like Skill Challenges, with "utility" actions players have access to that actually interface with those rules a little bit, would do wonders here. E.g. an action that lets you take a risk (increase DC maybe? Or roll with disadvantage?) to potentially get two successes instead of one with certain skills. An action that lets you give up your turn to allow an ally to reroll their failed check under certain circumstances. Of course, these would need limits and testing (you most assuredly know by now how much of a fan I am of testing and statistical analysis of new rules), but you can see how these don't have to be massively complex to still be engaging as a gameplay exercise in a way "DM says" is not and cannot be.
I don't think so? I have very little experience with Fate so I can't really respond to that.
Only if you force every rule to be a discrete, individual rule for every single situation. Abstractions allow us to cover an infinite variety in finite space, and with some of the improvements the community developed (e.g. the "Obsidian" SC system), they truly sing already—assuming a creative DM, of course, but this thread has already told me that that assumption is mandatory anyway, so it is safe to make. Just a little bit more, and it would be golden.
And, note, I'm not saying this should replace literally all possible skill usage ever. Personally, I'm of the opinion that we need a combat equivalent of "just a couple skill checks" (I refer to this as "skirmish" rules) that can still have some sting, but which can be resolved in 5, maybe 10 minutes at absolute most. That way, when all you really need is one single skill check, you have it. But for things like "negotiate with the Queen" or "navigate this dense forest", you also have rules that turn that into an interactive and interesting gameplay experience. And, likewise, you have rules for complex and challenging combat scenarios, "set pieces" where the point is to enjoy the combat for its own sake, AND rules for "literally just fighting four goblins in a room" where the point is to make an obstacle, not a challenge that is engaging in and of itself.
These rules are not some pie in the sky pipe dream. They are not transforming D&D into a radically different game, nor stapling a different game on top of the existing one. They are, at least in my not-so-humble opinion, making the game actually deliver on its promise of being an engaging roleplaying game of exploration, socialization, and discovery, as opposed to a combat game that also involves begging the DM to approve your roleplay proposals.
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