I didn't study at any such high-profile universities, and my initial touching points with graduates from top universities did not exactly lead me to believe they were anything special, apart from their parents wealth. Most of them had an MA or even PHD that was paid for in high tuition fees. They did not feel anymore intelligent or educated than the average person I meet, and they did not do anything particularly interesting.
Then later I had the pleasure of spending some time with true outliers, who usually also studied at top universities. Some of them would be obsessed with their field of study, and seriously work 80 hours a week on papers and projects. Some of them seem like completely normal people, with social lives and hobbies, and then you see the work they do and are just blown away at the genius they put in there somehow.
And then there are the behemoths; you can throw any topic at them, and they will say something interesting. There are few things more mindboggling and intimidating than introducing someone to a topic you are intimately familiar with, and they basically immediately answer one of your open questions, while asking a much more interesting and deep question regarding the topic.
You can find geniuses anywhere, but in my limited experience, there's a much higher density of these kinds of people at these places. But, because of how the top universities are structured, the inverse isn't true: Going to a top university does not make you better.
A Ph.D. is something that anyone can do with a bit of patience and effort. Does that mean we should shift the bar so it means professors are geniuses? No. I don't think any arbitrary qualifications make you a genius.
I think that depends on the field and on your definition of “anyone.” I’d bet against an average 100 spatial/math IQ person being able to get a PhD in math or physics, even if hardworking and patient. They would probably be something like 2.5 standard deviations below average and while IQ is not the end-all and be-all, such a vast gap would make it extremely hard for them.
I think the bar should go much higher, somewhere around Feynman. And remember that’s low according to Feynman’s own standards: he didn’t see himself as a genius.
If that’s your definition of genius you have to raise your standards.
”The world is filled with educated fools and uneducated genuises.” – Richard Feynman