I think part of the issue is that the queen has reigned for so long we hardly see her as a person in her own right any more (which is a major issue for me in itself - kind of revolting for someone to lose their individuality and personal agency like that). She's just a figurehead, a talisman. She represents stuff but she doesn't do anything or change anything.
But she is a person. She's an old lady who could tell us all to naff orf and go and live out the rest of her life in comfortable obscurity if she wanted to.
And then we get her eldest son.
And if he said "nah, no thanks" we'd get his eldest son. And if he said "actually, I want to keep on being a pilot so stuff your crown" we'd get a toddler.
And if the parents of that toddler said "hang on a minute, we don't want an accident of birth affecting the choices of our son, it's obscene to pile that sort of expectation and attention on the head of a two year old - leave him alone" (they probably woudn't be allowed to do that, but if they were), we'd get Harry. Who wouldn't be all that happy, so if he said no we'd get Andrew.
I'm guessing at that point, if not before, the whole edifice would come crashing down, but maybe not. How far back in the dregs of some cadet branch would you be willing to accept your monarch if the House of Windsor woke up to the realisation that they could still have as much money as they would ever need but without the hassle if they told us to shove our constitutional monarch up our collective arses?