I have a strong opinion on this topic: a potential advisor must have an excellent reason to refuse to advise a graduate student who meets certain minimal requirements. The department has accepted the student. Presumably the student has successfully passed prelim exams, etc. The department as a whole has promised to help the student in their pursuit of a PhD. In my opinion, it is inappropriate to tell a student that, although the department promised to help, I personally think you do not deserve / warrant my advice. There are obvious exceptions: too many current advisees, personality conflicts leading to unhealthy working relationship, etc. Agreeing to advise is not a guarantee that the student will make progress, and if they do not, both parties should re-evaluate the relationship. However, faculty have an obligation to the PhD candidates admitted to the program. They should accept advisees unless there is an excellent reason to refuse.