Throwaway: I have a PhD in CS, and I wouldn't describe myself as very intelligent.
Maybe slightly above average. I am constantly amazed at how quickly others in my team can understand extremely complex mathematical problems in a few seconds. I would need at least an hour of quiet thinking, and I struggled a lot with the mathematical aspects of my PhD. But I
did work my ass off for 5 years (mostly out of curiosity, though, there was no family pressure, my father is a builder and my mother worked in a supermarket).
Something I noticed: extremely smart people have a tendency to see a problem and quickly sketch the solution in their head, or sketch a proof that the problem cannot be solved. Their overwhelming life experience is that they are always the most intelligent person in the room and that their intuition is always right, and so they quickly mark this problem as "done" / "boring" / "unsolvable". In contrast, people with curiosity but less intellectual confidence tend to experiment with ideas to see if they would work / why they wouldn't work / if they work to a certain degree. I certainly do, and everything I have ever written a paper about, including my dissertation, was discovered during such experiments. If anything, I have a PhD in intellectual naivety.
I know of several extremely smart people in PhD programs who have not produced anything interesting in years, because they shrug off every problem as trivial, see paper writing as below their dignity, and keep themselves busy with teaching. They seem to wait to be automatically rewarded for their intelligence. After all, that is exactly what happened to them in school, and during their Bachelor/Master studies.