I'm Irish, although I live in the UK at the moment, so naturally I am a little biased against the monarchy, but honestly, I don't see what they actually contribute to British life beyond a bit of PR, something for the Daily Mail to write about and a substantial security bill every year for the taxpayer. Much of the "work" they undoubtedly do is part of the PR thing, rather than any vital contribution to the wellbeing of the state.
I don't begrudge the Queen (or Prince Charles) any of the wealth in itself, but to have somebody so wealthy in charge of ANY state in this time is inappropriate. This is the era of the middle classes (and it has been since the 40s), like it or not, and to have a relic from a frankly now irrelevant past STILL the head of both the state and the church is pointless, and contributes less to the national psyche than the chattering classes probably believe. An inspirational and well qualified elected president is far better equipped to represent the spirit of the current age.
To make it worse, the monarchy has not recognised its irrelevance, or perhaps better, inappropriateness (probably because the Queen is very old, and known to be a creature of habit), and it has not modernised in the way of other surviving European monarchies, which have pared back and toned the whole glitzy carriage/palaces thing back substantially, and behave more humbly and naturally.
Also, much like the papacy, the institution of monarchy was created at a time when you didn't realistically expect to be an unquestioned ruler for very long - if the people didn't want you, there would be a coup, a battle and off you go! Or if you WERE liked, you died of the flu in your 40's, or got bumped off on the battlefield during an invasion etc. The idea of a monarch (or pope) who JUST KEPT GOING, decade after decade after decade, was never considered (and Queens are far worse for this than Kings - women just keep on living!).
That was far longer than I meant it to be.