Actually quite a few people care about the UK having a king, in the UK. In Northern Ireland, there is a considerable republican (small "r" population) for political reasons.
The BBC promotes the monarchy heavily as it is under royal charter.
There were significant protests at the Queen's funeral cortege and the current king's coronation. The state clamped down hard, in one case arresting someone for holding up a blank bit of paper.
I admit UK wasn't the best example as now it's freedom of speech is maybe worse than in Russia or China. But I feel like public does not trat it as the biggest issue of the UK at the moment.
Let's say Denmark for example.