1. It's been around a long time.
2. In pre-democratic societies it saved argument if power passed from father to son. Only it never really did (save arguments I mean) and the history of monarchy is all about pretenders and rival claims and rebellions and assassinations and civil wars.
3. A special virtue passes down the bloodline. It is a wonderful, mystical thing. I mean, just look at Prince Charles and see how wondrously mystical he is.
So the Queen stands up in front of the Commonwealth heads of state and says she trusts they'll give the job of fronting the organisation to her elderly eldest son (the aforementioned Prince Charles) once she's in the cold, cold ground- and- while I don't suppose it matters terribly much- I hope they turn round and say, "You ain't boss of us any more and actually we have minds of our own...."