The threat is of wealth becoming political power and the government becoming an oligarchy... which has happened in the US, as shown by the recent study Northwestern and Princeton. When the few have the majority of the influence, that is no longer democracy, and there is no reason to believe that the control exerted by the wealthiest players is made for the benefit of those at the bottom. This a flaw of government more than of capitalism itself, but it's a flaw nonetheless, seeing as the two — capitalism and government — are intertwined.
I agree with you, of course. Though I'd say it's not just wealth, but political clout and "connectedness" as well. There are quite a few influential community/union leaders that aren't all that wealthy, but command a great deal of political power. Both by virtue of the people who they "lead" and the contacts they have in various levels of government.
What I'm trying to point out with the above is that: We are already assuming that the wealthy have a selfish or non-altruistic motive behind their actions, simply by virtue of them having wealth. If we go down that route, then we essentially need to admit that the problem isn't that the wealthy are selfish, but that their wealth enables them to exert that selfishness much more.
You are most certainly right that this is a flaw of government, or democracy in general. However, it is not a flaw of capitalism. It is, in fact, a virtue of capitalism: that money represents our "vote". But that vote doesn't magically stay with us, it get's transferred every time we "vote", or buy things.
They don't have to be intertwined, Anarchocapitalism seeks to do away with the institution of political authority entirely to deal with this problem, for example. This absolutely terrifies the kinds of people who don't understand that the state is the cause of the problems with capitalism because they always attempt to address the problems by handing more political authority to the state, which sells it off in a process of regulatory capture.
You assume that these people are trying to address problems with capitalism and not, you know, quality of life. That's exactly like saying that an atheist is simply angry at God when the majority of atheists don't even think God exists.
These people invariably see "hand more power to the state and petition for more aggressive control of the free market" as the solution to increasing their quality of life, or whatever else they're trying to accomplish.
What difference do their goals make if their suggestions are always the same and guaranteed to turn out badly?