Actually, the US Federal government is also only a currency user, ever since 1913. The US Dept of the Treasury has no legal authority to create new US Dollars
The so-called independence of the Fed is all smoke and mirrors. The Fed was created by Congress, it has to operate under the rules set by Congress, and it can be undone by Congress. More importantly, even today the Fed does not operate independently from the Treasury. The Fed and Treasury coordinate their transactions to enable the Fed to manage the bonds market. Seriously, read up on it.
a pseudo-private/public institution whose owners are US banks but who is somewhat answerable to the US Congress and the President
That is quite misleading. Outside of regulatory capture (which is unfortunately a very real thing), the banks have exactly zero influence over the politics of the Fed. They are formally owners, but even the profit of the Fed is largely paid out to the Treasury.
This last point highlights just how absurd the institutional setup is, by the way. The profit of the Fed is in large part due to interest that the Treasury pays to the Fed for the bonds that the Fed owns. The profit is then paid back to the Treasury. Hooray for smoke and mirrors bureaucracy!
should Congress remove that authority from the Federal Reserve (...) in the middle of the mess we're seeing, it would bring about an economic panic that would dwarf any we've heretofore witnessed.
Oh, really. Never mind the fact that such an action wouldn't even be necessary, what form do you imagine this economic panic would take? I assume it'll be like the panic that happened after Treasuries were downgraded to AA+?
Greece, Ireland, and others are all perfectly able to coin their own money at will. They need only abdicate treaties prohibiting it and fire up the printing presses. The reason they haven't done so is that it's economic suicide.
Bad comparison, because Greece and Ireland are in a very different situation. Their problem, especially in the case of Greece, is that its currency should have devalued significantly relatively to currencies of the rest of the world, but that was prevented because Greece tied itself to the Euro. Countries that do not have pegged currencies don't suffer from the same problem, because their exchange rates never go that far off-kilter.
That said, I would say that reintroducing their own currency is in fact the best thing Greece can do economically. Better to have a very painful but short cut followed by a swift recovery, than to suffer many years of economic depression. Argentina is a good example that this can work.
We've seen in Germany, Zimbabwe, and many others what happens when you attempt to coin your way out of a massive fiscal debt.
I was wondering when the inflation bogeyman would show up. Hyperinflation in Germany and Zimbabwe was never about printing too much money; that was just the spectacular side effect of other, very different problems. This is a good introductory paper. Tl;dr: in both cases, a collapse of productive capacity combined with foreign currency-denominated debts created an impossible situation. Printing money was a symptom rather than a cause.
What happens when the US pays more in debt servicing than its entire annual revenue combined and we begin borrowing for 100% of spending plus x% of the debt servicing?
Since that can only happen due to the interest that the government pays on the debt, the answer is very simple: decrease the interest rate. The interest rate is a political choice set by the Fed, after all.
If the decreasing interest rate should cause people to buy and invest instead of saving, even better: This will cause tax revenue to go up endogenously, thus driving the deficit down and ending the situation that you fear so much. If this process goes so quick as to create inflationary pressures, then MMT also prescribes a clear solution: Raise taxes in a targeted way to force the economy to cool down.