No, it's both.

The purpose of high school is to give you a wide foundation on everything.

The purpose of an undergraduate degree (in math) is to give you a wide foundation (in math).

In a (math) PhD, you are generally hyper-specialized in a very, very narrow area (of math).

Although the end goal of a PhD is a specialized thesis, the first couple of years generally involves courses with a wide coverage of analysis and algebra at the graduate level.

Given her achievements, I'd be very surprised if Cairo hasn't already covered the material in an undergrad degree

This is the entire premise of a liberal arts education. Not everyone pursues one, but it's certainly well-represented at the tertiary education level.

I've not studied this, but my guess is that the liberal arts education as the foundation is necessary to allow young people a chance to figure out who they are. I certainly found this to be true for me and would guess for my closest college friends.

If a young person is exceptional, do we force them into a liberal arts box? Surely there is value in literature and history. But this one young woman had found her passion. I have to believe that is she found out about something else, she would take that on.

Maybe. What interested me at 17 certainly does not interest me now.