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.
Look at all the presidential systems in the rest of the Americas, they're all mega fucked and third world. Of course the USA Empire is also currently collapsing.
Parliamentary democracy has a better track record, for sure.