1) "Conservatism" these days would arguably be a US phenomenon as leading democracy in the Anglophone world. They certainly didn't get started supporting a monarchy.

2) And it is really interesting to note that, while I think monarchies are stupid, it was a remarkably good strategy. As far as I know (my history might be about to betray me) the UK didn't have an equivalent of the Terror after the French revolution or the period where the French killed off people like Lavoisier. To say nothing of the debacles in places like Russia (Communists) or Germany (Nazis) when they moved away from monarchism.

The UK probably should get rid of the King; but in hindsight a slow transition is arguably the cleverer path. It is a complex topic; the aristocrats in Europe are systematically underwhelming.