+Douglas Cole penned a post recently, Character Study - why focus on combat? He writes about developing an effective combat character within the rules of the game. Go check it out and the previous post where he discusses his paladin in 5E (which I fireballed last session and rolled the best damn damage I'd ever thrown, of course the dragon was immune, but poor Marcus was not).
My take on this is very similar, my characters need to be combat ready. +Rob Conley runs a medieval fantasy with lots of ancient Roman influences. While there is a lot of roleplaying, there is also a lot of combat. Rarely do you get anywhere without a weapon in your hand. Or several hundred other behind you with weapons in their hands. Like Doug mentioned, it takes a special player/group that won't take action during combat. The majority of the rules of nearly all fantasy game are for the organization of combat.
I have played one character I can think of where I played a non-combatant. But my character was incredibly rich (we were playing 3E GURPS at the time and I plowed 50 points inn wealth) and ran one arm of a thieves guild. He didn't have any combat ability to speak of, but he had a lot of people around him that did.
+Zzarchov Kowolski's game, Neoclassical Geek Revival has a completely different take on combat. I had the fortune of playing in his game a time or two, but in his game, if an encounter ends in combat it is considered a failed encounter. Whoa! Took me a while to wrap my head around that concept, but I loved how it played out. But his system is not combat oriented so it made it easier to avoid a bloody conflict.
In this most recent 5e game I've played three characters so far. The first two went off to do their own thing. I had Sidwin, a rogue who's ideals did not match with where the party was going so he went his own way. While he did not shy away from combat, it had to be for the right reason. A rogue with a moral compass if you will.
Then there was my lizardman gladiator, Leshar. He was only around for a few sessions, but he was all about the combat of course. Loud and brash. He burned down a keep and battle the sheriffs elite guards as the world burned around him. It was the best day of his life. He soon parted company with the party because as soon as we defeated the sheriff and his men, we handed over the keys to the place to another adventuring party. Leshar found the secret way into the keep and got out with a hefty fortune and left town before the party gave that away to the other adventuring party.
Finally I have a mage. A timid mage who is not good at confrontation. Combat makes him nervous and is scares him to cast fireball. And after he murderized the party paladin last week he's going to like casting it less.
I've rambled off topic. But I believe where systems are built primarily to resolve combat its difficult not to gear a character towards it. Can it done? Of course. And it would be challenging for both the GM and the player. And even more difficult with a party to succeed in a combat-adverse campaign. But that would be an interesting game.