The UK monarchy has pretty much no power as it is. Prime minister says sign this.. gets signed. What we really have is a full family of ambassadors who work from day one with no retirement (only death) that costs ~£36m per year. Which considering what they do is a fair deal
People still seem to be under this whole "monarchy costs us money" cloud but the civil list generates income for the treasury and the Crown estates are allocated a % of said profit only. Also despite common misconception you could not just remove them and claim the lands in the civil list as most of it is owned by the monarchy directly. It is just managed by govnt.
Personally i think how we have it set up is a nice way to be. We have a head of state + family, who does what they need to do whilst not getting involved in politics and costing not so much.
Think of it like removing all power from the US president and changing the way the upper house works so that they don't pander to politics and pass/reject bills based on if they are actually good for the nation rather than trying to score points.