To those who endorse an elected head-of-state - i.e. a president - this would cost a good deal more to implement than the monarchy does at present. And they would also have very little power, so all that extra expense would go nowhere but to make a half-arsed moral point that doesn't actually have widespread popular support. And that same head-of-state would still get 'money back' from the system (as someone earlier put it).
Is the monarch-headed system perfect? No, far from it. I'd surprised if anyone was arguing that there are no problems with it, but from a financial perspective it makes sense, and from a cultural or traditional perspective it makes sense. The only perspective from which it doesn't is conceivably a moral one, and even there the grounding is rather iffy.
If one has a bee in their bonnet over aristocratic privelige, might I suggest focusing efforts on something a bit more useful or important, such as, say, reform of the House of Lords?