Why haven’t the monarchy lost their heads? Do they really need these in-breds sitting around high on the hog and doing absolutely nothing?
See 17: Eliza worked as a mechanic. Her grandsons served honorably overseas.
Son Charles can peer through a knothole, suffering no loss of depth perception.
A serious answer for you - the way the British constitution has developed, the existence of the Monarchy is the most fundamental break on a Prime Minister or Parliament becoming tyrannical. If the Monarchy was abolished, there would be no clear constitutional power to stop a Prime Minister from refusing to go to an election, or to resign if he or she lost the confidence of the House, for example.
Because of the existence of the Monarchy and the knowledge that the Monarch would step in, if a government ever exceeded its authority, no British government has actually done so, so it can easily look like the Monarchy serves no purpose. But it's very existence and the power to step in keeps things stable.
You can actually see this if you look at the Commonwealth countries - because while it hasn't happened in the UK, it has actually happened in reasonably recent history in some of the Commonwealth Realms, where governments have tried to exceed their authority and powers, and only been stopped because the Crown (in the form of the King or Queen's representative in those countries, the Governor General or a Governor) stepped in. The best example of this occurred in Australia in 1975 - not that long ago at all, really. A socialist Prime Minister (Gough Whitlam) and his Labor government wound up unable to effectively govern the country because of a series of fairly complicated events I won't go into, leaving him with no real constitutional choice but to ask for Parliament to be dissolved and for a new election to be called - something Whitlam did not want to do, because he knew he would lose (due to massive economic incompetence and corrupt behaviour on the parts of some of his Cabinet, even though he himself was probably not corrupt). The crisis actually reached the stage on 11th November 1975 that Sir John Kerr, the Governor General, the Queen's appointed representative in Australia - did have to intervene, and dismiss the entire Whitlam government from office appointing the Leader of the Opposition as temporary Prime Minister (having already established that he would immediately ask for an election). This is just one example - there are others - about how the powers of the Crown are essential to preventing a government or Prime Minister from exceeding their authority. They are the final brake.
They haven't had to have been as obviously used in the UK (although the Queen has actually used her powers on a handful of occasions - perhaps most notably when she used her powers as Queen to appoint Sir Alec Douglas-Holme Prime Minister in 1963, after the Conservative Party realised they didn't actually have an official method to choose a new leader and Prime Minister when Harold MacMillan became too ill to continue in office - the Queen agreed to use her reserve powers, but told them to come up with a process so this wouldn't happen again - an example of how the Monarch can use her influence to make a process more democratic), but the still exist and they still matter. After the 2010 election, when the Labor government under Gordon Brown lost their majority, Brown initially remained as Prime Minister while David Cameron (Conservative) tried to negotiate a coalition deal with Nick Clegg (Liberal Democrats). What Brown said to Nick Clegg in a phone call just before he resigned is telling:
"Nick, Nick. I can't hold on any longer. Nick. I've got to go to the palace. The country expects me to do that. I have to go. The Queen expects me to go. I can't hold on any longer."
We do not know if the Queen had actually spoken to Gordon Brown, because such a conversation, by convention, would be kept private - but even if she hadn't, he was quite rightly describing the constitutional situation. He did the right thing, so she did not have to intervene - and hopefully, most British Prime Ministers would do the same. But if they ever don't...
(It works the other way as well - the British Parliament can remove the Monarch, or, in fact, dissolve the entire Monarchy, by a simple vote - so a Monarch also cannot act as a tyrant - it is a genuine balance of powers.)
This probably isn't a system anybody would design from scratch if they were trying to design a new system of government. It's one that has developed over quite literally a thousand years into one that currently gives the United Kingdom an extremely stable government - you don't mess with that lightly. It would not be impossible to change it, but it would not be easy and nobody is sure that what would emerge would work better. The US has made a republican system work very well, but it was designed by genius patriots - can you see any James Madisons or Thomas Jeffersons among those in charge of the UK today?