But if the federal government is the one borrowing that money from itself (the Fed), it is much cheaper.

Then you're assuming that an entity that gets all the money it asks for at low interest rates is going to spend it efficiently and not have that cause price inflation. This is the opposite of what we see in practice when we e.g. subsidize student loans.

You're also then taking on all of the risk that the investors had been. You could pay millions of dollars and then lose it to anything from an act of terrorism to having bought a million dollar piece of equipment (or five thousand of them in five thousand hospitals) that then become obsolete overnight when someone releases a phone app that can replace it. But when that happens and you bonded against the government's credit, there is no filing bankruptcy to clear the debt, you still owe all the money even if what you bought with it is now worthless.