Combat is important, but it's far from the most important aspect of the game. I certainly don't want to spend the majority of the game session engaged in combat.
I just saw a quote in a thread where someone said combat occupied 90% of their campaign. This comment jarred me a bit, because in my best campaigns I think we are pushing 20-30% combat. It makes me wonder how it is possible to unify these two play styles.
I think 4e sort of exacerbated the problem my mostly only providing rules for combat and adventures that provided little in non combat challenge (except for the odd skill challenge).
I think that 4e exacerbated the problem, not because of a focus on combat rules, but simply because combat takes a very long time, even at 1st level. Grid-based combat, frequent forced movement, interrupts and triggered actions, high monster hit point totals, and each player having half a dozen options each turn make for a tactically rich game, but it also makes combat take a very long time.
In the first few 4e sessions that I ran, I don't think that we were able to finish any combat encounters in less than an hour. Some of them took 90 minutes. After a bit of a break, I incorporated some of the Essentials material and newer monster math. We all had a bit more experience with the game and these changes probably helped, but the encounters were still taking about 45 minutes on average (level 2 party at this point).
We would play for about 4 to 5 hours, once every two or three weeks. Three encounters in a session would end up taking 75% of the time we had available. Because each combat took the better part of an hour, the players would often have a discussion about "okay, so what were we doing again?"
I ran a couple of sessions of Basic D&D and one session of AD&D 1e for this same group, and we didn't have any of these problems. Battles took about 10 to 15 minutes on average, and we could have half a dozen combats in a session without taking more than about 25% of the total play time.
The format used in published 4e adventures also bears some responsibility, as the presentation really draws focus to the encounters. Even one of the better 4e adventures has a situation where the PCs fight a group of enemies outside a portal, then use the key on the portal to teleport into a room and fight some more enemies. Then they go into the adjacent room and fight the "boss" encounter. There are no other rooms in this "dungeon," so they just teleport back. That sequence would take us an entire evening to play through, and there is virtually no gameplay outside of three back-to-back encounters.