Obviously not and no one would agree to that. If the son of the Emir of Qatar is living privately here in the US- either the Emir and/or the Qatari government should foot the security bill, same thing if Prince Sverre Magnus of Norway decides to live in the US- his security should be taken care of by either the Norwegian government or his grandfather or father...I hope you get the picture.
Princess Madeleine of Sweden lives in Florida and Sweden doesn't pay for her security. When she was single and lived in Sweden as the youngest daughter of the King, she didn't have full-time security either, but was provided security only when performing official royal duties. That is the norm in most Royal Houses nowadays.
Honestly I can't even imagine how British police for example would operate in the United States outside their national jurisdiction. Would that be even legally possible ? Or are you suggesting that the British taxpayer should pay for private security for the Sussexes in the US?