I concur, I think there's something wrong with a big nation doing this. (Smaller nations run sovereign wealth funds all the time.)
The FED (more or less) sets the interest rates that the US government has to pay; though if they tried to buy everything, we would see inflation. I suspect the actual failure mode is a different one: real wealth is limited by productivity. If the government is buying all the stocks, we have just shifted ownership around, but don't actually increase productivity. Productivity might even drop, because the government is probably not a good activist shareholder.
For real estate, there's a decent argument to be made that the government should buy it all, and lease it out for a few decades at a time to the highest bidder.
The FED (more or less) sets the interest rates that the US government has to pay; though if they tried to buy everything, we would see inflation. I suspect the actual failure mode is a different one: real wealth is limited by productivity. If the government is buying all the stocks, we have just shifted ownership around, but don't actually increase productivity. Productivity might even drop, because the government is probably not a good activist shareholder.
For real estate, there's a decent argument to be made that the government should buy it all, and lease it out for a few decades at a time to the highest bidder.