I guess ones' experiences depend on the groups you played with. Obviously, with the "right" group of people, any of the PnP rpgs could be played "theatrically" even when they all have stats/charts/tables/dice. I just played with people who were more into numbers. (Over my pnp career, I've played D&D/AD&D, Shadowrun, Rolemaster/Rulemonster/Rollmaster :rofl: , Runequest, Call of Cthulhu, and a few others. Ars Magica was probably the least number-y. The only no-RNG rpg that I'm familiar with was the Chronicles of Amber rpg, but I didn't play that one, only knew some folks who did.)
Really don't put tabletop miniatures games (played more than a few of those, too) in the same category, since they're about one person maneuvering masses of generic troops against another person, not several people with single customized characters against the plot & conflicts that a referee confronts them with. :shrug:
With that experience, I guess you're familiar with the (not excellent, but relatively useful) threefold model?
You are right, every PnP can be played in all sorts of ways, and in Threefold terms most cRPGs are very much "gamist" as opposed to "dramatist" or "simulationist". As it happens, the latter two are closer to what I want, but you pretty much understood that anyway.
What I believe is that all three playing styles and their variations could be easily included into a game like this, for example with difficulty and realism sliders. Eating and drinking for the simulationists - can be turned off for those who don't care. Deep story and background for the dramatists - can be ignored by those who don't care (as it already was in the previous Elder Scrolls games). Lots of skills, combat, and heroism for the gamists - number of enemies and deadliness of combat can be changed for those who're rather challenged in every fight. A damatist might not be interested in constant fighting and lower the number of encounters and size of enemy groups. A simulationist might turn the realism slider up so that these numbers are only perfectly logical, and would turn the combat realism slider up so that every fight is very dangerous - of course that'd mean that the game would, on that realism setting, offer aid by friendly units or something in larger battles, who are not just red-shirts to instantly die.
It really wouldn't take much effort. The game'd just ask you a few questions at the beginning to find out what playing style you like. You could even try different approaches to see how they work out, increasing replayability. And with people like myself being more interested in the game, it'd also not be bad for sales.