It's not the Middle Ages and these days, the monarchy isn't seen to exist because they are better. They're public servants who can't chase any of their own dreams or develop any talents they might have, because they're busy doing endlessly boring engagements to support the country and boost morale, which they do for many people they visit, and they charm other countries who may have hostile intentions towards us. They do so by hosting those countries at BP state dinners and by going on official visits, where they do more boring engagements.
Yes, they have huge wealth, but why would they devote their lives to boring public service and no retirement otherwise, and life in a goldfish bowl where the whole world's media and social media is jeering at you and criticising you and hoping to gain embarrassing private information about you that they can beam across the world.
The monarchy does an enormous amount for charity. The Prince's Trust has helped hundreds and hundreds of troubled youths get back on their feet, and that's just one example. There are many more.
Finally, the monarchy provides an over-arching stability that no politician is above. Some people don't like the monarchy, but is having a greasy politician as top dog really any better? Remember the Trump presidency??
For me, there's a romance in the long, long traditions of monarchy too. Republics have no pageantry, no glamour, no mystery, and no sparkle. They're comprised of grey politicians and underwhelming public events.