So common in academia! The student writes a detailed, error-checked, well-edited long email only to receive an answer like
'yes plaese
Sent from my iPhone'
Definitely a 'I'm very busy look at me' powermove
Actually they probably are that busy and aren’t trying to impress students, they’re trying to grade a bunch of exams while reviewing a paper while writing up research while writing a grant and also having a personal life.
And if they treat them all with this degree of attention, then they're probably failing at all of them.
The grant writing and (supervising the work of the people performing and writing up) the research funded by the grants that will also be the basis on which they will secure future grants get more attention, obviously.
Many, perhaps most, successful academics are horrible mentors and parents/spouses. That isn’t pertinent to the fact that all faculty are, in fact, quite busy.