I think we've been very lucky with the current Queen, and that is why people like me agree with Ego that essentially the monarchy is outdated and hard to justify in a democratic 21st century society. HOWEVER on a practical level I don't have any appetite for disbanding the monarchy at this moment, I don't think it would be good for the country.
The current Queen has been pretty great in terms of being such a stoical, apolitical, inoffensive-and-reserved-but-still-charming Head of State. Her offspring however large don't seem to have the same qualities. I do think that when Charles ascends, and 21st century Britain is faced with a much less appealing monarch, the approval ratings will surely go down and everything thrown into question.
The financial aspect TBH to me isn't a big enough factor either way to get excited about. There are arguments on both sides for whether the Royals cost more than they generate. I think the ideological aspect is more important.
Personal preference aside, how many people here would bet that the monarchy would still be in place at the end if the century? Or would you bet against it? It's interesting to consider...not sure which way I'd place my money.