Is the cost of their upkeep any less than it would be to maintain all their estates via English Heritage
plus the cost of a Presidency and his palace, AND the cost of an election every four fucking years?

I doubt it.
( Grrrmachine the indifference engine, Sun 3 Jun 2012, 21:20, archived)

Royal family annual cost: £40 million a year.
Total Cost of All White House Elements, for fiscal year 2008: $1,592,875,254
apparently
$200M a year just for Air Force One...

I don't think we need to worry too much about how much they cost us. It's like the cost of a first class stamp for everyone in the country.
( Moon Girl Technologies horrendous beanbag, Sun 3 Jun 2012, 21:31, archived)

The Crown Estate pumps around £300 million a year to the Government.

( Mu Dinofiddler, Sun 3 Jun 2012, 21:44, archived)

It wouldn't much worry me if they didn't.
It costs about 2 billion a year just to run the Inland Revenue.
( Moon Girl Technologies horrendous beanbag, Sun 3 Jun 2012, 21:56, archived)