The United States having a Monarchy would be unthinkable, but in Europe, a system like the British is probably the best system at least as it pertains to having a non-political head of state. If one is worried about the expense, then trim some of the fat (which Charles wants to do anyway IIRC).
There have been times recently, where I wished we had a non-political head of state.
There was a time early on during the revolutionary period when this set-up was still possible had King George III accepted the Olive Branch Petition. We would be more like Canada today had there been such a reconciliation between Britain and the American colonies.