To me it is just an irrelevance and mostly still around because it attracts visitors to the UK, allows people to fawn over others, and people like the connection to our history - even if this has as much bad as good in it.
How many visitors does the royal family actually attract, though?
I mean, I get that we can see visitor totals for Buckingham Palace or wherever, but how many of them came to the UK
because of the monarchy and how many of them would have come to the UK anyhow and would have happily gone to the British Museum, the London Eye, or done a Thames sightseeing cruise instead if the Palace hadn't been open?
The Palace wasn't even open to tourists until after the 1992 fire (my quick Googling says the restoration took 5 years, so I'm assuming that it opened to the public in 1997, but I can't confirm). Did this cause a bump in tourism for the nation as a whole?
Is there any other measurable data that says, "yes, more people visit the UK because it has an active monarchy?"
I think I know a grand total of 3 people who would ever want to do a "royal pilgrimage" to the UK, which is a fraction of the number I know who would want to do a distillery tour of Scotland, and nowhere near how many would want to go for a big stage show in London or Edinborough Fringe.
Like, from where I sit, it seems like getting rid of the monarchy would have about the same impact on British tourism as the closure of the Port Ellen Distillery did... if the net effect is even negative at all.