We currently have no capitalist societies on earth.
That said, I do find the Equity Fund idea interesting, though it's not entirely clear what this looks like in practice, especially for the unbanked, the mentally ill, homeless people, etc. who might not really know what to do with shares, since some of them don't really know what to do with cash, either. Seems to me these are the people most in need of uplift, no?
I'm not too worried about most lawyers getting automated out of a job anytime soon, after all, to the extent where I want to see the economy overturned for the likes of them.
I think we overweight how many people in society do not know what to do with cash. I think we may say that we believe they can do something better with it and sure perhaps, but it is bold to believe one knows what to do better with another's resources.
To a lesser extent, similar things can be said about your other examples.
How are the artificial mega cities in China doing? Didn't they build several cities from scratch that are supposed to house several million people each?
About all the things you listed - housing, transportation, education, food and travel are being impacted by digitization and AI.