Government debt is a result of government spending into the real economy. It is where we get the taxpayer dollars that we spend, some of which go back to the government itself. A government without debt is also an economy without money.

Governments with central banks can mismanage their currency, but they can't run out of it.

There's a body of government explicitly built to do exactly that and given exactly that power in the constitution. It's called Congress.

If we are broke then why do people buy our debt? It's obviously more complex than you make it sound.