I think the queen has fulfilled the function of a benevolent, non-political Head of State very well since her accession in 1952. Despite the attempts of her family members to destroy her reputation she has remained a stable, matriarchal-style figurehead for almost seventy years, and it’s undeniable that, rightly or wrongly, she’s regarded with respect and affection by a large percentage of the population.

However, for many of the reasons stated by Steve above, I would prefer an Irish-style symbolic, non-political, elected President with a term limited by statute. It seems to work very well for Ireland, and I can see no reason why it wouldn’t work for the UK too, always assuming that there is a UK in the future - by no means a certainty. I’m sure it won’t happen in what’s left of my lifetime, but perhaps within the next fifty years...?