I believe that their days are numbered because we don’t need them and the concept of monarchy is a relic of the past, celebrate the history but we can do better in the future. I don’t mind the queen so much, if it was my decision I’d let her see out her reign and then call it a day. I get some of them are likeable, but some are hideous. However, if we had a referendum on the monarchy today the public would vote to keep it, but I think more and more people are questioning them and Charles could have a very tough time if he is caught meddling. It may happen quickly or it could take a century, but I’m pretty sure they’re on the way out.
I’ll be echoing BoroMart but it’s well reported that the Queen influences policy before parliament and there are secrecy laws in place so we can’t see the extent of their influence. Don’t take my word for it though, there plenty a quick google search will bring up plenty of what’s known... it’s the unknown we should be a bit more worried about.