Capitalism would collapse within a socialist system because of simple economics. Profit comes from the difference between what workers are paid and what they produce. In socialism they would get all they produce, while in capitalism they would be getting less, so there is no reason they would choose capitalism if it just puts authority over them and they make less money lmao.
Capitalism can only exist within a state structure because they can only maintain control of property through a monopoly of force. Capitalists are simply control of the means of production by an outside source. The capitalist is only defined in relation to the worker they control. Look at the Hegelian dialectics of the master and slave for an understanding of that one
Your assumptions that capitalism would collapse doesn't matter in that regard, it only matters if you would let those Ancaps have their voluntary capitalistic society.
If that society would collapse in the end, fine.
Voluntaryist Ancaps have the same assumptions about a socialist system: that it will collapse eventually. However, they would let those voluntary socialists or communists have their way.