I was reminded of this discussion when I saw the news of King Juan Carlos's of Spain's abdication today. There's few arguments that can be made in favour of a monarchy, and no-one can really say that, beginning from a tabula rasa, you would rationally chose to have a country ruled by a head of state chosen by accident of birth. All the same, Juan Carlos's actions in the attempted 1981 coup make the best possible case that can possibly be made for this basically irrational way of running a country - he represented a non-political reservoir of power that could take action where no-one else could, and he acted decisively.
Personally, however, I have to admit that my own support for the monarchy in the UK comes mostly from the gut. I certainly believe that, given that we are where we are there is no point in changing now, and that there are economic and constitutional advantages to having a monarchy, but in the end my support comes from history and tradition.
Occasionally I get accused of not understanding the emotional commitment that some Chinese people have to the Communist Party. Believe me, I get it - but "getting it" and being able to excuse it are two different things.