I don’t see any problem with monarchies: after all, plenty of countries, in Benelux, Scandinavia and various Dominions, are ruled by monarch and are vastly better than some republics (PR China, Brazil, Egypt).
But which dynasty would rule in the United States? Apart from some Eastern and Southern states, there is no tradition of nobility, whether de jure or de facto, and the only one I could see to pull it (Washington) flatly refused.