Well, the first reason is that most state governments[0] do not have anywhere near enough money in their accounts to get a return that will replace the revenue stream they get today through taxes. You might be able to build it over time by reinvesting budget surpluses.

The other problem I foresee is that the market is fickle. The S&P 500 reached a level in the second half of 2000 that it would not see again for over 14 years[1]. Any investment that needs to generate consistent revenue isn't going to have nearly the growth rate over the long haul that an index fund would provide. That makes the initial investment requirement significantly larger.

But otherwise, I am okay with the government owning a lot of private enterprise via index funds, so long as it has exactly the same voting power that I have. Which is to say, none.

[0] In case anyone needed the clarification, this whole discussion is about state governments; it does not really apply to the federal government for obvious reasons.

[1] Adjusted for inflation. The index did recover to the same number in 2007 just before dropping 50% in 2008.