“Respectable math graduate schools, mostly, do not even have MS program for pure math!”
Clearly you haven’t looked at Part iii math then. It’s a very common destination for Churchill scholars as preparation before a PhD (see their comments here: https://churchillscholarship.org/documents/Part3MathematicsforChurchillScholars.pdf) and attracts many of the best mathematicians in the world.
As @astrotemp points out, US undergrad degrees are broader and therefore have less depth in a specific major. For example Berkeley requires a total of 13 courses for a math major. At Cambridge a maths undergrad will usually take 8 maths courses per year for 3 years.
That level of preparation, combined with Part iii, allows for completion of a PhD in 3 years. I think the US system, where it often takes 6-8 years to complete a PhD, is crazily long in comparison. I was done with my PhD by my 24th birthday and could then happily get on with my life far more quickly than would have been the case in the US.
It seems your son is focused mainly on “research and publishing papers” in math and is trying to get through Berkeley undergrad as quickly as possible (in 2 years?). I’m not sure why. Have you thought about how his academic career would progress through and beyond a PhD? He’s clearly brilliant, so I have no idea why he wouldn’t insist on doing a PhD with the best mathematicians in the world and ensure he has the best possible preparation to get into such a program.