Because we like our royals, and they don't cost us millions, no moren than having a president style head of state would. If they were such a bad thing then why did so many countrys around the world opt to keep them when they got independence.
Also your missing the benefit of having a head of state that isn't elected who knows the goings on of the last 60 years of government, who isn't chasing votes, her experience and advice is invaluable to any prime minister. In fact all the prime ministers have said how important the weekly meetings are to them, being able to discuss matters and know they are not going to be leaked to the press, or that she's not going to try to score political points out of it etc etc