Well, I think it's all interrelated.
I've found that civility is a lot more effective than people tend to give it credit for. But I do civility reasonably well. A lot of people don't do it well--they can't maintain a robust distinction between civility and acquiescence, or between civility and indifference.
We don't demand civility, and so people practice it less, and so they're worse at it, and so it makes less sense to demand it, so we demand it less, so people practice it less, so....
The problem, in part, is that we don't use it enough. The tool lies there unused, and we lose the skill to employ it.
It's not just a value-neutral choice of tool, either. The effectiveness of incivility is decoupled from its truth-value. Strongly-worded expressions of anger or scorn draw attention, and shift mood, but they do so regardless of whether the attitude corresponds to any deeper reality.
In contrast, civility itself is pleasant--which has a modest impact, I expect, in a truth-independent way--but mostly just unlocks our ability to use reason (as you nicely describe).
So there is another cost to incivility, a personal cost: by employing it, one decouples one's impact from one's correctness. It's a "get out of the constraints of reality for free" card. I'm not sure I agree, therefore, with your idea of civility as a form of credit that uses up some capital. To the contrary, I think incivility consumes one's own moral and intellectual capital, while civility is neutral or pays dividends.
But you make a good point that sometimes, all the civility in the world does no good, and only action can rectify a situation. I suppose that, at times, the best form for that action to take is being uncivil.