In my bones I am not a monarchist.
Personally, I find rank and status simply because of who you are, or your ancestors were, is totally wrong. Having said all that, I cannot think who a UK president could be. Nobody springs to mind who is liked by many and has integrity. Most politicians fall at the first fence as many are in it for personal gain and are born liars.
Queen Elizabeth of the UK has been monarch for most of my life. I cannot remember anyone else. By comparison, her son Charles has a lot of respect to gain.
No, Queen Elizabeth is not perfect, but during her long reign she has commanded respect.