Some things are important because of their symbolic value, and the British monarchy may very well be one of these things. Sure, it absorbs a lot of the wealth of the country, but a lot of other things do the same thing without as much payoff. The morale of the country might not be as high without this kind of symbolic rule.
An American to debate whether England should have a monarchy is no more relevant than whether England should debate whether American should keep the White House, but just for the sake of argument I can toss my ideas into this mix. The monarchy, which over the years has relinquished its political influence to possibly less than the Kennedys in America, is still a major draw and source of fascination with England. I have never seen statistics but I would imagine the enthralled tourists must at least contribute enough to make an impact on the cost of keeping the monarchy. When a member screws up they do find it embarrassing but that is all part of the rabid interest we cannot keep away from, and helps define the character and personality of the country.
Yes, there have been good kings and queens of england, but they did not earn their position. They became kings and queens because they happened to be born into the right families. I think there is more honor in a kindergarten graduation than the coronation of a king. A kindergarten actually had to work for a school year to graduate from kindergarten, while king just had to be born to the right family.
Many people who support the monarchy admit the benefits of democratic rule in Britain. Many also admit that the monarchy have abused their power in the past- and to be fair, so have people elected into power. Yet through their support of democracy, they effectively render their argument for maintaining an obsolete institution to a matter of emotion, loosely defined "tradition", and image.
It is WE THE PEOPLE who forced the monarchy to curb their excesses and to allow elected officials to create the laws in this country. So how can someone say "Well, they don't do any harm?"- WE forced them to relinquish their powers over the people! One cannot say, "Well the Queen chooses not to do X Y or Z," when the reaction would be largely negative- and has been at least since the time of Oliver Cromwell, who was one of the main proponents of modern day Democracy in British history.
The idea that someone should "rule" in a country that purports to be democratic is ludicrous and entirely contradictory. The idea that being born into a special family should give you the RIGHT to rule is even worse- along with the reality that the taxpayer subsidises a life of luxury for those who have done nothing to earn it. Now whilst democratically elected politicians are far from perfect, they are not infallible; we the people can remove them through our right to vote. Such freedoms are not protected under a monarchy, regardless of whether they have much power or not. The truth is, we do not need them! We have Parliament to make our laws, and everyone there is voted for by the public. The Queen's remaining powers are largely obsolete, so why should she have them if they bear no consequence on the people's lives? Furthermore, of what use is the Royal Family if their only functions consist of well-publicised visits, skilled hand-waving and various projects designed to cover up the fact that they do very little from day to day?
Democracy is the fairest principle, and the best way of government. It is not perfect, but the provision for freedom of speech and association, as well as the right to choose our leaders trumps the idea of unearned privilege, which is what the monarchy represents.