It sounds like some in the UK wish the residents of the US envied them their royal overlords. Not so. Americans like to visit to take a look-see at the bounty your royals have raked in, but never would wish for such a relationship with powerful unelected individuals. (It's bad enough these days with rich industrial leaders - who needs royals?)

Mexico tried it and it didn't turn out well. At. All. "Off with his head" unwell. They could have executed him for his facial hair alone. By this time, Texas had fought itself free of Mexico, and there is no way Texas would have craved a UK overlord. In this instance, you can safely assume that as Texas goes, so goes the rest of the US.

The Hawaiians had royal rulers and from reports I've heard, wanted to keep them. But the US interferred. President Denali had a hand in that particularly bungled appropriation of sovereign lands. As you can see, the tumultuous history, briefly represented here, shows no inclination for the weight of an overlord royal family. Disabuse yourself of the idea.