The FAA is supposed to catch problems before the crashes, not after them. It's pure luck that a 737 Max didn't crash in the US, that doesn't in any way absolve the FAA of it's charter and responsibility to check Boeing's activity and it's failure to assess the risk of the 737 Max. Our FAA did put US citizens at risk when it approved the 737 Max, so the FAA is on the hook
absolutely.
Your point about Ethiopia's and Indonesia's agencies (and airlines) is reasonable, they ought to do their own due diligence on the aircraft that they use & allow on their turf. Smaller countries and agencies with fewer resources than us have tended to trust our FAA and the aircraft manufacturers to assess these risks. In that sense, the FAA's failure to regulate the Max and it's policy of outsourcing regulations to the manufacturers themselves is (rightly so) truly embarrassing for the FAA, is resulting in loss of trust of the US FAA globally, and maybe on the bright side is going to cause all other countries to start doing more of their own due diligence.