Corporate profits come from somewhere. It would be a switch from an income tax to a (hidden) federal consumption tax.

The initial money to pay for stock has to come from somewhere, and that somewhere would be more debt or traditional taxes.

The federal government would control the companies (assuming it acquires majority shares), even if government employees aren't staffing them. That's socialism.

Socialism/communism is bad because if given the opportunity for direct control, government can't help tinkering in business affairs to score political points, rather than because it makes the business better.

Other than raising the money, that doesn't seem too hard to solve. The Federal Reserve could buy index funds and be a passive investor like everyone else.

I'm reminded of Matt Levine's running joke (?) about whether or not index funds are socialism.