I think you greatly underestimate how much the rich depend on constant state action to remain that way for more than a few hours.
My country has thousands of pages of regulations and half a dozen federal agencies whose reason for existence is protecting passive corporate investors against their own hired management.
Corporations large and impersonal enough to need hired managers are a relatively recent innovation. In every industry, diseconomies of scale kick in at different levels, and function as natural limits to corporate growth; but lobbying and regulatory capture allow companies to grow well past these natural limits, and establish oligopolies that extract market rents greatly in excess of what they could by pleasing customers.
If the state and the courts ceased to recognise limited-liability corporations, the level of inequality would implode immediately. No risk-free passive investment would force wealthy parasites to get useful jobs.
Then, if we cut government spending by a good 99%...