I have seen many capitalists support higher taxes on the rich. It really depends on the specific flavor of capitalism one advocates: technically, both social democracy and libertarianism are subsets of capitalism, but they differ significantly from each other.
I think the Cold War-era propaganda of "pull yourself up by the bootstraps" and the idea that the US is a real "meritocracy" have contributed a lot to the notion that advocating for higher taxes on the rich is necessarily a negative thing or a sign of entitlement or "laziness." These ideas, in my understanding, are not as common in some other capitalist and hybrid-economy countries like Germany, Sweden, France, etc.
I think in past eras, there was greater support for liberal social programs and the labor movement, as it turned out to be a major stabilizing influence against the extremist ideologies which arose in other states.
Of course, the "pull yourself up by the bootstraps" and the illusion of "liberty and justice for all" have always been around as cultural and political tropes. There's also been a work ethic which has existed, particularly in Middle American farm country that "everyone has to do their share of the work." But it was often a family affair where, at the end of the day, they all get to sit and eat at the same table. They might also do business at the nearby town, where there are shopkeepers, tradesmen, and others offering goods and services. It seems natural that, since they're doing the work, they get to own their own stuff and keep the spoils of their hard work.
That's how many people might perceive a free market economy, since that's what they're more inclined to see in their everyday lives. Of course, that also entailed a certain wariness about hucksters, carpetbaggers, snake-oil salesmen, grifters - which were viewed as hazards within a free society, but avoidable if one is vigilant and aware enough. But as they say, "a fool and his money are soon parted." That's another little pearl of wisdom which is part of the general capitalist perception, which is tantamount to blaming the victim. Just because someone is a fool, that doesn't give anyone the right to con them or manipulate them into buying something they don't want or need - or signing a contract that's not in their best interests.