Of course an elected president would be cheaper: we wouldn't have to keep his, or her, mother, father, brothers, sisters, children, grandchildren...etc as well. And we wouldn't have to pay for all the ridiculous ceremonies - stating with a coronation - which are supposed to be so traditional and ancient but probably for the most part date back around a century; all contrived to make the monarch seem ever so majestic. And waste money training the males for a military career which they will never really enter.
I'm not quite sure what a constitutional monarch actually is...does it mean that her son can interfer with democratic planning processes? And pass oppinions on agriculture, alternative medicine and architecture - in which he has no training - which are taken seriously only because he is who he is?
The problem is we cut off the king's head about 100 years too soon and then didn't know quite what to do; most people - with a few exceptions - couldn't get their heads around the idea of a republic. We nearly got King Oliver and then we still had the ridiculous hereditary process which gave us Tumbled Down Dick. If only we'd had Protector Lambert. The French got their timing right.
Yes David Attenborough, Joanna Lumley, Richard Dawkins, Helena Kennedy, Lisa Jardine, Frank Bruno, A C Grayling, Claire Rayner would all make good candidates...and Martin Carthy.