Except the kind of economic relationships they were advocating were not remotely like what you see in the case of anarcho-capitalism as we know it. The idea of competition went hand in hand with other ones like worker democracy (advocated by among other people John Stewart Mill and the Owenites) and cooperative ownership (co-operatives sprung up all over the US from the 1830s all the way up to the 1880s ranging from utopian communes to more practical agricultural organizations). They were talking, like later socialist anarchists like Bakunin, about liberation from all forms of oppression and not just from politically-empowered tyrants. There was an understanding and emphasis on collective good in the philosophy, just not one that was handled via the mediation of the state.
Many of the more famous individualist anarchists
were Owenites. They learned from the failures of the Owenite communities, especially New Harmony, and reimagined their ideology to take into account the lessons they picked up.
Even for the ones that weren't involved there, laissez-faire was in the air as an ideology, and not just one of the powerful. Benthamites were
the intellectual heavy-weights of the pre-Spring of Nations Western World. The
main difference between, say, Leggett and a modern anarcho-capitalist is that Leggett still believed, to some extent, in the monopoly of force that defines modern states. And this guy was
the public voice of Jacksonianism in New York City.
The great, the rich, the powerful, those people that you're saying generate a reaction? They already existed in many places in the Northern United States in the 1830's and 40's. Their society goes right back to the Revolution. And in this time?
They were National Republicans/Whigs. That's
why the Democrats could be so successful in a North that was, at best, apathetic about slavery: The planters cast themselves as the champion of the average American against the overweening Money Power. The Bank War gave Andrew Jackson, already the most popular man in the country, a kind of frenzied popular support that you only get today for an FDR or a Reagan.
The Northern Democrats of the time? They bought into the idea that the
state was why the Money Power had so much power over regular people. The tariffs, the corrupt use of public funds for canals and railroads, the over all financial system (including the publicly chartered banks, up to and including the Bank of the United States),
that was what the average joe on the streets of New York, Philadelphia, and Boston didn't like. They had no problem with the idea of private property -- most could remember a time as recently as last the generation when their family lived as small-holding farmers or as artisans, those with family history as factory or dock workers or as sailors remembered when their labor was in such high demand that they could get virtually any price they asked for it. They had no problem with trade, both inside the country and with the wider world.
It was the people going off to live in communes, the utopian socialists, who were the fringe movement of well-off middle- and upper-class young adults. Even then a lot of them converted over time, as the utopian communes collapsed and they found the religious communes distasteful. It was only in the late 19th century, after the nationalists had won pretty much everywhere, that the radicals were marginalized and began drifting into the socialist camp to try to find any relevance whatsoever. Even then they survived as an ideological tendency (Tucker, Meulen, fr. ex.).
This is
ripe pickings for PoDs for what the OP is asking for.
This is very different from anarcho-capitalism. All anarcho-capitalism wants is the abolishing, or at least severe limiting, of the state and allowing market forces to dictate all other social relations. Anarcho-capitalism sees no problem with wealth inequality, corporate ownership, and private profit at the expense of all other goals. The only thing that needs liberating here is profit from the power of the state, not people from the whims of the powerful. Collective good in anarcho-capitalism, as we know it OTL, is defined purely in terms of rational self-interest and in practice the ancap system is probably better described as economic feudalism. You aren't going to get people like Murray Rothbard, who said Franco's fascist victory in Spain and subsequent White Terror was excusable because he was killing communists in spite of fascism being one of the most statist ideologies in existence, springing up from the Owenite movement, Spooner, or other individuals or tendencies like that. It's just not there; to get something we'd recognize as anarcho-capitalism it needs to happen during or after the Second Industrial Revolution and in the age of Morgan, zaibatsus, and Krupp.
You see, this is the real problem. You're smuggling in an intense dislike of modern anarcho-capitalists, throwing around the deepest ideological aspersions you can think of because you've built your own political beliefs around
just how wrong these people are. I'm not going to tell you that your political beliefs are wrong, this isn't the place for that, but the sociology you've built them on, in part,
is wrong.
You don't need to go to the 20th century to find people enamored of laissez-faire, you've got it right there, with the Jeffersonians and the Jacksonians and the radical liberals the world over. Most of them weren't extremists, of course not, most of them were OK with this or that intervention because they thought it was beneficial to them,
but this is still the breeding ground you need to be searching through to find what the OP is looking for. Push more people toward the extreme one way or another and this challenge is perfectly completable.
EDIT: And, of course, what you're talking about essentially did exist already, the essence of 'fuck you got mine' is there in Stirner and the Egoists. They only really had any influence in the US, however, after the Civil War.
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