This would be a recipe for further corruption. And of course the govt would have a monopoly on this and will not be accountable for any screw-ups.
The way these things rruns is by having an elected board from the employee/retirees to oversee the professional money manager performance. They also have guidelines, 50% in government bonds, 20% in corporate bonds, 10% in utility stocks, 10% in blue chips, and so on. SAFE INVESTMENT PORTOFOLIO! If you let Joe blow do his own investment, and he wants to be FREE to do what he wants, he will gamble, and 90% will lose, and then come back crying to the government to feed him.