There's basically two archetype pacifist roles in a TES game:

The guy who is morally good, a conscientious objector etc.

And the guy who is simply too weak to fight for himself (whether he is morally a pacifist is irrelevant since his game style is the same for the most part).

Either of these roles will not engage in some grand campaign, unless he cant help it at all. The former may know self defense and survive and the latter will die most likely when confronted by epic obstacles. The former is against war and violence by choice and the latter is impotent to the matter outright. Once you become a crusader for good, or whatever your intent is, you lose the role of pacifist. Same as if you become a big shot and have other people do it for you (unless you use calm spells on your henchmen to keep the beatings to a minimum), you still become more than a pacifist though, since your getting involved in the grand scheme of things.

Are all the kids finished with their "hurr durr violence!!"?

Cool. Yes OP, I can see where you're coming from. In Fallout: New Vegas I played a non violent doctor. It worked out pretty well actually with only a few close calls.

I would love to play a monk/healer guy who only uses his fists for non lethal combat.

wow, some people really lack imagination... anyway, on the topic, I think its a great idea.
Pacifist type quests, or quests with non combat solutions sounds great,and I can think of plenty of fun ways they could make each playthru something different and interesting.

Stuff like being a detective and sneak around town (literally if your a thief) following the smithy because his wife thinks he's cheating on her and she wants to know who it is, only you find out he is actually discreetly purchasing a bunch of packages from odd merchants... Further investigation reveals a the packages are acually part of an aniversary gift he is planning to make for his wife... do you tell her and spoil the secret???

Or investigating the strange goings at a baking drive to raise money for the local chapel. Did the snarky old argonian Vrooshsa lace Neldam Arelas' rubarb pies with a laxative compound in a fit of jeallousy or was it a result of poor quality rubarbs supplied by the Arijani cubs?

And who doesn't want to cure VD's at the local tavern for a fee??? hours of fun in hearing the NPC explain how they got that particular rash.

There is plenty of scope for fun and true-to-lore quests that can be compleated without combat if the writers at Beth studios care to spend some time with it.