I would take a more materialistic approach. No country has monetary policy autonomy. The bogey must be a stable exchange rate, which means that the country must choose financial repression or sound monetary policy. Thus, monetary policy autonomy does not imply a useful privilege to engage in stupid monetary policy. So, what, exactly, do we mean by “autonomy”?
Think of driving on a highway with guardrails. You have “control” of the vehicle, but you cannot make it go around traffic or through traffic or over traffic or faster than traffic. And you may not even be able to make it go slower than traffic lest someone bump you from behind. You can phrase this problem as “you can’t choose both the road and the speed you will travel on it,” but that assumes that there are an infinite number of good roads to good places, when, in fact, the choice of roads is limited, and they all have traffic.
Yes, there are temptations to control capital flows, and it is important to recognize that some regimes will do that. But those regimes cannot issue a reserve currency, because the world knows they will eventually float their money with unpredictable consequence. Issuing a reserve currency is the holy grail of sovereign achievement. Bad money drives out good, so if you can issue the best money in the world, people will hold it and lend it back to you at a bargain rate. A successful economic polity maintains a stable exchange rate by allowing free flow of capital and practicing sound monetary policy. Everything else is bush league.
As regards MMT, much is written about it, but its key message is easy to state: Thanks to advances in technology, the money supply can now safely grow more rapidly tomorrow than the GDP grew yesterday. MMT has always been true, but it has not been relevant, because more reductive approximations have been adequately predictive under conditions of high marginal cost (aka scarcity). MMT becomes relevant when marginal costs falls (aka abundance). Then, approximations like debt/GDP prove unduly constricting. It now matters that the output gap is way bigger than people think and is getting bigger all the time. And MMT says so.