[MENTION=42582]pemerton[/MENTION]
You responded with two interesting points that I wanted to address.
1. I was somewhat presupposing combat and roleplaying were not entirely overlapping (I wouldn't go so far as to say exclusive though). I think I still do. There is certainly some roleplaying in combat. In more interesting storylines there's even more (like when a villain switches sides or a pc decides to provide mercy, etc etc). However, I think that most of the richer roleplaying happens out of combat.
In my experience combat causes three things to occur that inhibit roleplaying (not attacking 4e here, this is from my 2e and 3e experience mainly):
a.) Focus on powers/abilities/numbers like hp, etc...Focus on the rules.
b.) Turn based play.
c.) Lack of meaningful character decisions.
a.) Focus on the rules is an effective way to engage in combat, and being effective in the life or death component of a game is rewarded by virtue of not losing. I've observed my players shift from roleplaying in an immersive sense to strategic gaming where they are moving pieces, calculating strategy, moving in absurd ways to avoid attacks of opportunity, etc. I don't blame them. That's not to say this happens every combat or even throughout an entire combat. But it does happen. It does not happen when they are chatting with the local lord or arguing for their lives at a trial.
b.) Turn based play. This one's really simple. Out of combat people feel more simultaneously engaged. They can act at any point in the "round" and, in fact, there may not be "rounds" per se. In combat, most of the time, the only meaningful actions are interrupts and those you take on your turn. Beyond that it's merely shouting a word or two here and there. Again, not always. Sometimes a player might engage in some lengthy roleplaying in combat, even while others are rolling, but this is more the exception than the rule.
c.) Lack of meaningful character decisions. Of course the decisions you make in combat affect life and death. That's not what I'm referring to here. I'm referring to character decisions. Give two players the exact same character sheet, but with totally different backstories and personalities. In combat, assuming they have similar strategies, you won't really notice a difference. Out of combat, you will see them make a number of very different decisions on how to approach NPCs, problems, what to do, where to go, etc.
2.) How would I fix it?
The thing I probably like least in gaming is when there is a "combat mode" and a "noncombat mode". I hate the idea of "encounter powers", and I don't think 4e did enough to get rid of dailies. I'd do two things to reduce both the nova and the fighter/wizard disparity.
a.) Get rid of "dailies". I've never liked them. I was perfectly happy playing 3e warlocks and binders to get my "magic" on. This is not to say that there can't be buildup or "big powers" for exciting, nova like moments. 4e does this nicely with action points. Resting actually can eliminate these, while pushing on grants more. I don't like that you can only use one per combat (that fits with my dislike of "combat mode"). Wizard spellcasting could use a more mana driven resource similar to these, and all classes could benefit from them to a degree, as they do now in 4e, but perhaps in different ways.
b.) Give everyone cool things to do out of combat. Note this is the opposite of what 4e has done, which is to somewhat strip out of combat for all classes, and give fighters more interesting things to do in combat. I'll agree that in 3e fighters had little on their sheets that made them cool in or out of combat, while wizards had plenty for both.
If I were designing 5e, I'd start watching movies. What cool things do "fighters" do in regards to noncombat roleplaying? I'd give fighters more skill points for things like intimidate, give them a reason to put points in charisma (because what movie action hero has a low charisma?), and in general provide a focus on awesome stuff out of combat. But these out of combat things would be useful/usable in combat on occasion as well (just like a wizard casting feather fall or hold portal).
Off the top of my head, a short list of fighter abilities, and the source:
John McClane (Die Hard): Intuition. He stays ahead of the bad guys, and he generally wins by figuring them out, even though outnumbered. This is also great in roleplaying senses. Is someone lying? Where are the bad guys likely to go next?
Doc Holliday (Tombstone): Gambling. Not just with cards, but with his own life, and taking risks in all sorts of social situations. Perhaps a luck meter or luck based powers would be appropriate here.
Ash (Army of Darkness): Inventiveness. His hand went bad. So he cut it off. Naturally. That was from the Evil Deads. In AoD he fashions a pneumatic metal hand. He uses high school chemistry to make bombs. He and the smith work to trick out his car into a helicopter death machine. Here the power would be some sort of science based or alchemy based abilites. But he's not awesome for these reasons, they're mostly how he fights. His quips and brash attitude are what make him awesome. That and his ability to form an army despite being a goof. These are charisma powers. I'm not entirely sure how they'd play out, but they sort of could fit with inventiveness. He takes the situation at hand, no matter how bizzare, and comes up with a quick and dirty solution. He's like a charming MacGyver, now that I think about it. I would want those sorts of powers both in and out of combat if I played a fighter modeled after Ash.
I guess that what I'd want to see would be for fighters to have powers (and perhaps a massive revamp of the skill system). However, I don't want mainly combat powers, which is the direction things have moved in across all editions. I want lots of cool out of combat powers for fighters as well.
I also want the line dividing combat and non combat to be erased.