That sounds plausible! I use the terminology for lack of anything better that also has currency. I'm not wedded to it, though.“Objective DC” and “Subjective DC” don’t get to the heart of the matter for me and also seem to have a bunch of baggage attached to the terms that further cloud things.
I agree with all this.In the Dwarf and forge example, I imagine in the “objective DC” system you would look for an already established DC that indicates super hot – say resisting the heat of Hell – and set the DC close to that. But you’re right, that doesn’t take into consideration the PCs narrative place in the world. When the Dwarf makes the Endurance check it’s not really a straight up ‘can my skin handle this fire’. It’s more like ‘can this Dwarven paragon of XYZ pit himself against the forces of Moradin’s fire and magic forge and prevail’. There are ways to model this in the “objective system” if you had an exhaustive list of DCs and/or modifiers say
Regular Forge DC20
Forge of Moradin +10
Paragon of Moradin sticking hands into a fire created by moradin-10
But the “subjective system” has already pre-loaded all these assumptions into the math. This pre-loading might be the essence of “subjective”. It’s more like “narratively empowered skill checks”.
The “subjective DC” system involves loose definitions of what a skill check can mean. Encourages you to make sure you’re in the right ballpark in terms of appropriate challenge, and then use the level appropriate DC that gives you higher levels of drama. It also certainly encourages the ‘just in time’ DMing you talk about.
If I've followed you correctly, I also think we agree that once you set about making it "objective" rather than "subjective" you lose some of that spontaneity and looseness around what a skill check can mean. (There can be benefits, too. As I've said upthread, I like Rolemaster and I like Burning Wheel. But these systems generally won't give you spontaneous action declarations like sticking the hands into the forge. They're more likely to give you very "grounded", nitty-gritty-of-the-gameworld-oriented action declarations. Different approaches for different play experiences!)