What it comes down to with someone like Weiner is that his public persona doesn't draw a bright line between politics and policy. Most Democrats treat that distinction as an impenetrable divide like the separation of church and state. At a theoretical level there's a legitimate argument for making that distinction. But at the practical level, most of the people who make the distinction between politics and policy are policy wonks who do so to shield themselves from the rough and tumble of politics.
What I like about Weiner is that he reacts publicly with the range of emotions that someone truly engaged in politics should react with. Politics can be maddening, stultifying, unjust, absurd, and crazy-making. That's why a lot of people hate politics, even people ostensibly in politics. But if you're going to really do politics, if you're going to engage on the battlefield, you have to grapple with all the maddening things that go along with it in order to get done what you actually want done.
Too many progressives seem to want to sit on the sidelines until someone, a Marquess of Queensberry, comes along and changes the rules of the game to make it more civilized. What they don't seem to grasp is that democratic politics are the Queensberry rules. They replaced mob rule. The fractiousness, unpredictability, and feralness of politics are vestiges that remind us of what the real alternatives to democracy are. The real alternative is not a debating club and smoking jackets.
What I like about Weiner, or at least what I see of him in public, is that he's in the game. He doesn't hold himself above it or outside of it. He's in there. He's fighting. A good lesson for Democrats: If you're actually in there fighting, you don't have to worry about "projecting" to voters that you're a fighter.