I don't think even more "oh, that fluffy stuff only the DM reads" chapters will change that perception.
I think what the game needs is cool non-combat stuff that draws the eyes of
players, not DMs. When you build your characters, there should be abilities and capabilites that makes you go "Oh, I want to buy/use/try that!"; more skills/powers/rituals/magic items purely aimed at the non-wargame part of the game. Or rules for that sake, like an roleplay-focused advantage/disadvantage system or something.
The article on Familiars in Dragon makes a good example. They had cool non-combat stuff they could do, and they had wonderful little roleplayable quirks listed.
The 4E rules set is the first rule set I encountered that I did not stop while leafing through and say "ooooh! I want to do that!" in regards to non-combat stuff...
(I did not do that on combat stuff either, but that is because I've burned myself out on MMOs, and want table-top RPGs to provide what you
cannot get in a computer game.)