If a corporation were to hire mercenaries to control a piece of land that they don't own, that corporation (if successful) would be the government of that land.

Their goal is still making profit, they just made your private property their private property. I don't want to go over libertarianism too, my only issue was with the claim

Capitalism is based on live and let live, meaning that nobody gets hurt by capitalism. The supposed injustices of capitalism are either a result of nature, or a result of government action

It's demonstrably false (unless you redefine capitalism), privately owned profit-based enterprises disregard your rights (including property rights) and will infringe them just as happily as any socialistic state. There is nothing intrinsic in capitalism that makes it "based on live and let live", when corporations can get away with fucking you up they do it, when they can't they can't because of external pressure (government).