The British monarchy, though it is flawed, generally has a sense of historical mission and loyalty to tradition that means they have psychological checks and balances which avoid the abuse of power. But it won’t always be this way, not when Charles gets in.
Presuming for a moment that the Queen didn’t kill Diana, the Royals largely stay out of politics. Their realm is ceremonial and constitutional. They are a useful fiction to hang power on and a focus for nationalism and patriotism. I’ve nothing too much against any of that. Not really “my bag”, but whatever gets your constitution though the night, eh?
The main problem with politics is checks the power of those in charge. This is why I think people supporting the coup in Egypt are fucking idiots. Most politics in developing countries is unimportant in the long run, what matters is getting that first democratic handover of power over. The more coups you have the further away from safety and wealth everyone is. It matters because it demonstrates that power can be checked.
In the UK there’s almost no chance of a democratic government not ceding power. Even Brown’s unsuccessful attempt to broker a totally constitutionally acceptable alliance with the Lib Dems was met with unease in Labour and without. The Royals similarly have largely avoided exercising what power they have despite few formal barriers to them doing so.
Not any longer, Charles has been using cash left intestate for his own charitable endeavours, showing a disregard for what he should do relative to what he is allowed to. Worse than that, his aides have been working within government exercising power that should be completely beyond the reach of an independent head of state.
Only a constitutional crisis really unseats a monarch, and people like to avoid these. The problem with monarchy is when the (currently effective) moral and cultural limits on royal power are gone there’s few formal ones to deploy. Formal checks are better than intermittent crises.