As far as I can judge there isn't a republic that has an office of the head of state that is more effective than our quirky, hereditary one. It may not be democratic or populist, but it has worked well enough for neigh on 1000 years.
Another truism: if it ain't broke, don't fix it.
The UK Monarchy is not broken, it just needs a bit of "Car SOS" treatment over the next 20 years.