...and such people must remember that they are there to serve us, and not vice versa.
Having met and spoken with many of the major royals plus more politicians than I can remember, I would say that on the basis of your criterion, we need to bin the elected officials immediately and keep the royals! Concern for the public is strong amongst the royals, concern for public opinion is strong amongst the politicians.
So, aside from the debunked reqasons concerning cost, public well-being/concern for the public and the erratic behaviour argument that doesn't stand the royals in any worse state that the politicos (rents boys and oranges in the mouth anyone?), what do you have against the monarchy?