It's hard to imagine of the UK or Canada, but it's a nice safety net. Perhaps easier to imagine of a smaller less developed Commonwealth nation (not an Australia joke!) - I can sort of see a tyrannical (and probably crucially also unpopular) leader getting overthrown that way if it were necessary; probably led by/combined with measures through other parliaments, i.e. military intervention.

I don't have one in mind, I don't think there's a likely one - there's an argument that it brings a sort of long-term stability that makes an actual application of its powers unnecessary, like a nuclear deterrent - I just think if there was some sort of unrest or rising dictatorial power in a state with ER as monarch 'we' would pay (even) more attention than otherwise?