Slowly they really have enough and easily could send us one back!
How about German chancellor?, French president? What do Scandinavian countries have? Do they have a constitutional monarchy or other? I really haven't looked. You can always find dodgy presidents but what about monarchs? It's a good thing the right wing king abdicated before his nazi sympathising rule got going. Looking back through time how does the monarchy stand up against modern dictators? The more their power got limited the better UK society got (not all related to that but who knows what the connections are).
Neither constitutional monarchy nor a Republic is perfect if the people at the top are far from perfect. However popular vote has to be better than privilege of birth to decide head of state. The latter is so arbitrary, from generation to generation you never know what you'll get. At least elected head of state can be replaced after their period of office. Bring in elections for monarch. Who would you vote for monarch? Charles, William, Princess Royal, David Walliams or stormzy?
The Mrs Merkel who has for a very long time been the stable presence in Europe and only in the last year been criticised for a policy based around humanity for those whose lives have been put at risk in their attempt to get the standard of living that a most Europeans take for granted. These people aren't criminals or terrorists but people using huge risks for the good of their and their family's future, being exploited by people smugglers and indeed some are leaving oppression too.
IMHO more should be taken in and by more EU countries. Instead they've helped to fund detention camps in Libya that's in the midst of a civil war.
If you're using the last year to write off the very stable leadership of ms Merkel I think you're being a bit selective about the matter.
As for Macron, is the French state and elected politicians any worse than our politicians? It's not the system that's causing the yellow vests to hit the streets. It's the reforms he's trying. Bear in mind many economists say the reforms he's putting through are needed to modernise the french economy. It's also kind of the norm for French citizens to protest especially if they're losing out or losing benefits / rights that are no longer affordable or right for the modern age.
As for stability being down to monarchy, in the EU all monarchies power is very much curtailed. Their parliaments and governments operate under the monarchy but in reality that's just lip service. If our monarchy was the cause of our stability then how does Brexit play out with that idea?
My view is actually that a fully elected Republic is better than a constitutional monarchy with an unelected upper chamber. The only issue with that is party self interest among the politicians. That's something present in constitutional monarchies too.