Why does a mathematics department want student evaluations of a famous professor?

Being a good teacher and being a good researcher are distinct skills. If someone has a job that requires both skills, they should be being evaluated on both.

Is this typically done at most American universities, irrespective of a professor's age, status or fame?

Yes. It's likely a required process of the administration, as negotiated in the faculty contract. It's probably not something your department has any say over; and in a case such as you describe, the resulting product is likely to be mostly ignored.

It's probably not worth anyone's time to hammer out every imaginable exceptional case to such procedures (the faculty contract and handbook, outlining procedures, is usually already mind-bendingly long). This is what work is like in a large institution; rules apply to all, and have many stakeholders, and not everyone gets their every whim or convenience satisfied.

I'm in Australia, and from my experience, almost every unit is evaluated every semester that it runs in pretty much all Australian universities. There might be a few exceptions, but this is just standard practice. The standard survey consists of a bunch of closed ended questions and then some open ended questions for more qualitative feedback.

From this perspective, there's nothing special about whether the instructor is a famous professor or a relatively unknown academic. Student evaluations are just a standard component of university life. It would be strange to make an exception, just because the professor is famous.

More generally, student evaluations serve a wide range of purposes and the relevance of most would not change whether or not the instructor is a famous professor. Such evaluations give the instructor feedback about how the unit was received by students. It can highlight areas for improvement. From a university perspective, it creates some accountability and some metrics that can be monitored.

Of course, there are also plenty of issues with student evaluations. And there is the potential if they are used inappropriately that they can create perverse incentives for instructors: e.g., simplifying education, grade inflation, and so on in order to have "happier students". But that's another issue.