but if they are no different to us then what makes them royal
Nothing. It's just smoke and mirrors. A clump of scrambled egg on a shpulder here. A tira there. A bit of pomp. A ladle full of circumstance. A heaped table spoon of pagenty. Ta-Da!
They bleed red just like everybody else. I know this to be true after my (ex) husband has a rather excitable nosebleed all over the kitchen floor.
The Kate Watching Fervouris based on something just as rare and valid as the blue blood "rariety". Cos just like the blue blood thing it's all in people's heads. Her appeal I think lies in the rariety of a Real Live Cinderella, ehich might be wuite enchanting if you are into that sort of thing.
Given that I kissed a Prince only to have him turn into a frog I am a bit off fairytales myself 
They won't go even if you sack them. They will lurk around getting the same crowds and media attention. Please see Emanuele Filiberto and his ilk as evidence. They got exiled for yonks after Italy went republic. The royal fascination didn't go away. And got worse when they were allowed back in, still sans offical titles. God god the man sang badly at San Remo and people STILL want to see his mug on the cover of Hello magazine (or whatever it's called in Italian).
And if they do get sacked the risk is they don't get replaced, but get joined..... by Mrs. President and all the flapping that goes on about whichever hapless women gets lumbered with that role.
I don't live in France but still got Carla "Coo Eee, back on the Front Page Again" Bruni shoved so far down my throat I damn near chocked on her.
Human appear to like having idols and FairyTale Representatives. Maybe it just adds a bit of glitter to an otherwise ordinary landscape ?
Even a lot of places without a clearly defined class system have a class system. Some people get to be more equal that others pretty much everywhere. All it takes is one ancestor in the place at the right time (like on the Mayflower) , and bobs your uncle, social kudos on a stick even centuraries later.