Our daily lives wouldn't change, but that's not the issue. The UK has a monarchy (like it or not) and they are still important people simply because of the office they hold - just like Boris Johnson. They get first-class medical care because that's what happens when you are at the top of the social tree in any country, just as these people never have to go to the shops, never do their own cleaning, never have to queue, get the best quality of travel every time they need to go somewhere. It's not fair, but fairness doesn't come into it when you're rich and famous.
And in any case, a lot of British people are still strong supporters of the monarchy. They're certainly not universally despised!