Charles is not liked especially after the revered late Queen
But I think that the Royal Family are in a bind in as much as he (Charles) has been promised the top job for so long that it would be difficult to force him to by-pass it and even more difficult to get Camilla to step down.
Plus the RF has had a plethora of problems the last few years so it will be case of don't make any waves
But it does remain possible that he will be given a certain time before he is pushed aside to enable the dream couple to take the job
Republic ?? I think that the demographic in Australia has changed and the people who hate the English are less now, after all as you say, find me a system that is better