I mean, you would be substantially increasing the size of government. The federal government currently employs about 3 million workers. The banking sector employs 1.4 million. To perform similar functions, the US government would need (at least) a similar number of employees. That is probably politically disagreeable.
They would be employees of the Fed, not the Federal Government, no? Also, I am not afraid of a big government so there’s that. Also, they would be paid well, but not get insane bonuses, etc. so that’s a distributive plus in my book (i.e., less wealth concentrated in a tumescent financial sector).