Capitalist anarchism doesn’t exist. Capitalism is a form of unjust hierarchy (or if you want to stick to the literal meaning of “anarchism”: capitalism is a way to create rulers)
There are capitalist anti-statists, bit being against states isn’t sufficient to make you an anarchist for above reasons.
Yeah. Wealth generates wealth. Wealth is power. You got born into a world owned mostly by the super rich, and therefore don’t have equal opportunities.
No amount of redistribution will prevent this state from re-emerging until wealth accumulation is made impossible.
It’s pure luck: even if the playing field gets completely leveled once, without systemic changed some people will luck out, get wealthy again, buy newspapers and apartment complexes and therefore monopolizes public expression of opinion and profit from living space.