In the UK we've been lucky with our royalty recently, but with a different roll of the genetic dice we'd have Randy Andy as king instead of Charles.

Anyway, you have kings, you just elect them and call the presidents, but they have basically the same political role and powers as George III did in the 1790s cut-and-pasted across. The USA needs to get itself a decent parliamentary system.

I'd argue almost the opposite: America's governing system (and the political culture of rejecting hereditary rule) is a big part of why it became so successful.

There's arguably a straight line from the Commonwealth's greater deference to inherited authority to today's tolerance of weak borders, stagnant growth, and declining economic mobility. A king seems like more of the thing that caused the problem, not the solution.

Have you read John Steinbeck's "The Short Reign of Pippin IV?" [0] All political sides in France frustrated decide to create a constitutional monarchy. The Communists supported the idea because it would give everyone something to revolt against.

[0]https://en.wikipedia.org/wiki/The_Short_Reign_of_Pippin_IV