Surely the people who send their children to Eton mostly love the idea of elitism and the sense of self-importance that it creates.
I don't agree with this. I went to Oxbridge (state school, council house); I was, and remain to a degree, a bit of a class warrior. I strongly dislike elitism and everything it stands for.
This said, I've met a lot of Old Etonians and Old Harrovians both at university and subsequently, and every one I've ever met has been utterly lovely: kind, gentle, decent, humble, and acutely aware of their privilege. On a class analysis I find the Eton bias in public life to be problematic. But, taking people as individuals, I've not found any of them to be remotely elitist or self-important at all.
The inference I draw is that (eg.) Boris is not an elitist cunt because he is an Old Etonian; it's because he's an elitist cunt. I speculate he would have ended up a (self-loathing) elitist cunt had he come from a more modest background.
Also, I found very many of the second-division public school types were arrogant elitist nobbers (the closest I've ever come to fisticuffs in my adult life was challenging an Old Pauline (ex-St-Pauls) who advised me that it was fine for his family to drink-drive as they had superior genes. He was being completely serious.)