The Queen may well get paid, but she also pays 70% tax on her whole estate - far higher than anyone else in the country. That's before you factor in that she brings a lot of money in from tourism. Lets also not forget that she is an amazing ambassador for this country - it doesn't matter who they are or where they are from, most people would be truely honoured to meet our Queen.
The Monarch is still important in today’s society; it ensures a non-political head of state and provides the final layer on the checks on Parliament. And as Churchill said, "While the Queen occupies the highest office of state, no one can take over the government. While she is head of the law, no politician can take over the courts. While she is ultimately in command of the Armed Forces, no would-be dictator can take over the Army." So far from being contrary to liberal-democracy (which is a sort of contradiction anyway) the Monarchy safeguards a liberal democracy as well as the country as a whole. In reality a Monarchy is irrelevant as to whether a nation is a liberal-democracy anyway, the Kingdom of Sweden is often sighted as some sort of liberal haven yet it is a Constitutional Monarchy.
I can think of three examples in recent times where a Constitutional Monarch (or royal representative) has averted disaster. First of all there is the 1975 Australian constitutional crisis. On this occasion the Governor-General, Sir John Kerr, dismissed the government of Gough Whitlam when the Senate withheld Supply to the government which made political deadlock. There is the recent Belgian Constitutional crisis where it looked as if the country was going to split in two, but the King, risking his throne, has sorted the whole mess out appointing interim governments and heading negotiations between the parties. Then there was in 1921 when the King, who had made his unhappiness at the behaviour of the Black and Tans in Ireland well known to his government, was dissatisfied with the official speech prepared for him for the opening of the new Parliament of Northern Ireland. King George read out his own speech on reconciliation which is widely credited as the catalyst of goodwill which led to a truce, ending the Anglo-Irish War. The reason for these uses of royal power stems from the Liberal thinking that men will always seek there own self interest. A Monarch is unique in that there own self interest is wholly intertwined with his kingdom, therefore a Monarch is always looking out for the best interests of the state and its people and as such is both a protector of democracy and the man to step in when democracy has failed.
The Figurehead role of the Monarch is much higher than that of an elected head of state, who is only there for 4 years and wont have anywhere near the same amount of respect or support both at home and abroad. The perfect head of state transcends class, race and politics and a Monarchy is the best way to get this. The best example for this concept is the Kingdom of Spain, the Spaniards have recently reinstated there monarchy as a uniting force for the nation where the wounds and divides from General Franco’s regime are still fresh.
Now to counteract these arguments you may point to America where the state is protected by separation of powers and the constitution. Yet the USA is unique in that it is essentially 50 countries united into one covering a vast geographical area. In a much smaller country like Britain a Labour man from Glasgow is, more or less, going to believe in the same things as a Labour man from London. This unites the party in a such away American party leaders can only hope for and make a party for more powerful. Now if the Lords and Monarch were replaced with an electoral system it is quite possible both houses and head of state may be controlled by one party, in such a situation that party could get away with just about anything including the re-writing of said constitution to suit there own needs. A case in point would be the French Republic, now on its 5th incarnation, each republic was safeguarded by a constitution and yet four of them have failed. I would be wary of vesting power into what it simply a pieced of paper, look what happened to the Treaty of Versailles.
Republicans always harp on about the cost of the monarchy, but this argument is fundamentally flawed. Tax money goes to the Queen only for official duties, house up-keep etc. The rest of the Royal Family have there own private estates or get money from the Queens Private estate. Furthermore; in return for the civil list the Government gets the revenue from the Crown Estate which is £190 million per year, much more than the £11.2m which the Queen gets on the civil list or the rather dubious cost estimate of £150m from the Republic group. But in reality the financial argument against the institution is irrelevant because a Presidents office would still have to be funded and the palaces maintained. However no matter which side of the argument you are on you must agree Britain’s constitutional future should be determined by finance.
Also to say the family do nothing is absurd, it’s published every day in the Times (Court Circular) what public duties royals are carrying out. There all over the place and do not get any public money for it, far better value than a single president.
I don't think class is that much of a big thing tbh