Absolutely nothing wrong with games like that! I feel you on player vs character charisma, and in backstory hooks and the like. Our DM really likes to hook our backstories into the game, and I frustrate him a little sometimes by usually keeping my background simple. Done right, the backstory hooks into current events, so it's not a "why are we doing this instead of the main quest" deal. Some of my favorite game memories are of conversations amongst the party characters dicussing what's going on with those hooks and helping the related character through it. I think it's really good for me though because our players are really good. We make sure that everyone gets involved, or if someone's not feeling it tonight we can steer more clear of them. We're not afraid to hand waive unimportant things, especially if/when the party gets split up. Everyone's really working together to make sure everyone's having a good time, and I feel like that's not as common as it should be.

Nothing against more strategy and combat focused games though! The teamwork is really what makes combat come alive in my opinion, and there's nothing more satisfying than a well laid plan coming together (except maybe everything going wrong and pulling it off anyways)