I have a friend who's doing a STEM PhD at one of the top programs - think e.g. Harvard / Princeton / MIT - and they are getting ready to drop out after the faculty there have told them that they don't have a real chance at academia since their published papers have been "too applied", and that strong work in theory was crucial. (They're trying to see whether the papers can somehow form a thesis, but they have mentally checked out and are looking forward to having a nice payday in industry.)
I wanted to know whether that is sort of the norm in STEM academia, that to have a real chance at becoming a professor, one should stay away from work that's "too applied", during their PhD years, and try to work on theory.
Is this generally true?