To those DMs that don't like using dice rolls in the non-combat part of their games:
Why do you use dice rolls in the combat part? If you want to reward good roleplaying by just saying "good job - you succeed", why not do that with good combat tactics also?
You ask an excellent question Z about something I've been working on for a long time. See the
Tactical Repertoire.
But in a more general sense I can answer this question in two basic ways because most of the other answers would be variations on these two.
1. To role play a skill challenge you must describe and or demonstrate your actions. You cannot demonstrate a combat against a dragon because no such thing really exists, and no human being can emulate hitting you with his three hundred pound tail, biting you with jaws that could in effect swallow you, grabbing you with claws that can completely encircle you and flying thirty yards up and then dropping you on your head to split your skull. You could describe your actions, and then dragons, but not demonstrate them or prove them by real action. So some things are beyond the realm of "normative role play" (which is a sort of assumed mental imagination based upon things we can all relate to, or at least conceive of) and into the realm of purely theoretical role-play (which is what math is really all about anyways, numbers are really just abstract images of real things, but the real things are rarely described, they are just assumed - you don't say 6+1017 what? you just usually say 6+1017 and assume the reality of your factors and answers.) Which leads to number two.
2. Enemies can counter your tactics. That is in situations of combat you are fighting living foes (for the most part, programmed automatons and undead notwithstanding) and therefore they can react, counter, and overcome even your best efforts. So it is not like an exercise against an "inanimate challenge."
So, because there are things basically beyond realistic role play (I say that with a certain sense of self-aware irony), and because enemies can counter your tactics and efforts, there must sometimes be a method of determining chance for things that cannot be empirically demonstrated, or for things that can be theoretically countered even if they were demonstrable.
However I have been working for a long time on a method of diceless combat for some combat situations.
Other situations, due to situational circumstances, I have not figured a way to totally eliminate the dice as a mechanical example/method of friction and resistance in combat role play.
But to reduce everything to unnecessary die play simply because certain aspects must be open to some method of chance or theoretical resolution is to totally misunderstand what role play actually is.
It's like saying because a man can move about in a wheelchair as an artificial means of travel then a wheelchair should be his only or best method of travel no matter what the circumstance.
Sometimes do what you are forced to do, or employ the only method available, but one should never confuse what one is forced to do with what is either natural, or best. Nor restrict oneself to what is artificial and limited, simply because that's the way the habit has evolved.
P.S.: By the way, I forgot to mention.
You can turn the question around and ask,
"Well, since combat is die rolled then why isn't everything die rolled?"
And then the implication becomes, well, why have a game in which any human capability on the part of the player is exercised at all, short of die rolling? Why not turn the game into a purely mathematical exercise in which chance determines every play aspect so that the point of the game then becomes
"rolling things and not doing stuff."