I agree there may be some social barriers, but, for instance 4 of the 10ish math students that started the phd program in pure math at the same as me were filte

I agree there may be some social barriers, but, for instance 4 of the 10ish math students that started the phd program in pure math at the same as me were filtered out by the written exams, another was pulled to industry in her second year, and another left due to (I think) not being able to finish their research before his funding ran out (had less due to entering with a masters). I could be forgetting someone, but I think I am the only one on the pure side, finishing at the 5 year mark in my program, and I put myself through some serious sleep deprivation to do it. The applied students seemed to do slightly better.