Get rid of the monarchy and then?
Just get rid - I'm sure enough volunteers can be found to be randomly selected to take a one-day turn at waving, cutting ribbons and signing things (that we must be, by convention, signed without protest). No more toadying subservience to hereditary privilege or special treatment, such as exclusions to laws or the ability to have proposed laws amended to suit before they are passed. The aristocracy should go at the same time.
Can't see why a ceremonial head of state is required in any event.