The Queen has no electoral mandate. So she only does ceremonial duties. As soon as you get a politician in that role, it fundamentally changes that role. Politicians are by their very nature, political. The current set up has a powerless figurehead, that does all of the pageantry in an apolitical manner. When you lose that, you get a figure that is far more divisive. Most of the people that would be driven to seek such an office, would then feel obligated to use that office.
The queen standing around waving means that those that actually govern don't have to do all of that malarkey. It's not how you would design it, but it works better than any of the alternatives that I could see Westminster devising.
Practically implementing a presidential system would be hugely divisive. People by and large are well disposed to the royal family, and they loathe politicians. It would make the Brexit debate look civil. It would be a truly loathsome campaign from both sides. And the cost is just not worth it. It would make no difference to the lives of the vast majority of the public. It would not save (or cost) any significant sums on a national scale. There is an idealogical case, but there are many more pressing issues that will be less acrimonious and enrich the lives of many more people.
Pretty much what I think. Economic arguments don't really work. We aren't paying to 'fix up her houses', the Crown estate is ultimately owned by the state, you and me if you like, albeit in a trust bound to the role. We are her landlord and employer, as you say we've just subcontracted the role of ceremonial head of state to one family company, Windsors Inc. We gain far more income from the crown estates (quantifiable) and the Royal family itself (unquantifiable) than we pay out via the civil list. Sure, she personally owns Balmoral and Sandringham and some swans and receives Ł40m a year from the civil list but to put it in context that's equivalent to just three Wayne Rooneys. And there's dozens of those fuckers, most of whom do fuck all for the rest of us.
I've never really understood the argument that with an elected head of state you get someone you don't want (the dreaded President Thatcher, Blair etc) but with an unelected head of state you get someone you do want. That seems a fundamental contradiction and one which places little faith in the people's ability to choose an appropriate head of state to represent them. Also winds me up when people want to express a preference for which member of the royal family they would like on the throne - "we should skip Charles and Camilla and go straight to William and Kate - they're so much younger and cooler". With a monarchy, you get no say. Period.
I suppose it's a question of whether you need or want a ceremonial head of state separate from the person who actually has to do the work of running the country. The US don't have one, by default it's the President and First Lady. Seems to work fine for them, but then again they vote for president with that in mind and you end up with the likes of Reagan or Trump, someone with charisma but with zero experience in the job and it's the party machinery and civil servants that make the decisions. I suppose that could work here, but I'd only accept it if it was a Michael Sheen rather than a Katie Hopkins. And the idea of the people choosing the ceremonial head of state, no thanks. We'd end up with Posh and Becks. Like Boaty McBoatface or Alexander Boris de Pfeffel Johnson as London Mayor, or putting 'Jedi' as a religion on the national census 'for a laugh' because it doesn't really matter. As for which of the Royal family we'd want on the throne next, of course we, or they, have a choice. We don't have a written constitution, we can make it up as we go along, I believe the rule of males having priority of succession has been scrapped relatively recently with little fuss (2011 I think?) so why not other changes to allow William or whoever to be the next monarch without creating a constitutional crisis?
None of this is to say I'm in favour of the monarchy as is, of course. I'm ambivalent about it and I'm more concerned about the EU referendum, the House of Lords, Tory gerrymandering, TTIP and the NHS, first past the post v PR, privatisation, tory austerity policies and many other things that will impact my life far more than some symbolic change to please ideologues.
And not to mention that in these turbulent times in the west, there are many lefty liberals like myself who look at the Scandinavian countries with their sustainable education, healthcare and welfare systems and smaller inequality gaps and are envious. Yet they have monarchies?