It's a good point, and I'm a slice of life fag too, so I agree with you in many ways. At the same time, I think the slice of life in Kurenai is so strong because the characters are so well developed, and I think the fight scenes raise some really unpleasant questions about their motivations, and who they are as people.
I particularly loved the first Shinkurou fight, where you see him just pouding away on these guys; no grace or style, just power. Thing is, he doesn't enjoy it, clearly, but there are still plenty of other ways to make a living. He's doing this for ultimately selfish reasons; he feels weak, and needs to prove that he isn't, which is hardly much of an excuse for kicking the shit out people. See episode three, where they show that he'll fight for money, but not to stick up for an old lady who's being abused. Sure, he has other reasons, but it still shows an interesting dichotomy in the character.
The ZOMG! DORAMA in Kurenai is wonderful because the characters are both tragic, and flawed. They have these horrible broken pasts (Shinkurou and Ginko are orphans, Yuuno is born to a family of killers, Murasaki lost her mother and lived in isolation, etc), but they also have very real, human weaknesses. Because they seem flawed and human we become so much more attached to them, and that makes the slice of life so much more powerful. You can't help but feel sorry for Murasaki, even when she's being a total bitch, because you can understand that she couldn't really have ended up any other way, and she's so obviously trying to be better. With Shinkurou I think it works the other way; we sympathise with his situation, but the cold brutality he sometimes displays means that we don't feel like we're being forced to like the guy just because he's a stereotypical "nice guy"