US is hybrid democratic socialist (progressive) and capitalist. (of the crony variety) These aren't opposites. Capitalism is economics, socialism is a planned government system. In fact socialism is never sustainable without some (but not truly free) capitalism to support it. Western Europe has figured this out for the most part, although I don't agree with that system. Democratic Socialist =/= Socialist, but the same laws of economics apply to both.

Socialism implies non-profit. Something done for the sake of "the people" even if it's a net drain. If the entities are for-profit companies it defeats the purpose. (I suppose some kind of "smart socialism" that makes money could exist, if you can figure that out.) Many companies do engage in socialistic type behaviors though, so for-profit entities may collaborate to do that. It would still be a hybrid.

IMO the ancap position should be to resist all non-voluntary uncompetitive state authority. That includes if the state is a cabal of private companies. ("corporations" couldn't really exist without some external "state" incorporating them)

I don't really care about ancom philosophy so I'll let someone else answer that. If someone wants to be a communist on their own property that's fine with me.