JeffE's answer here indicates that Masters degree holders are held to higher standards when it comes to graduate admissions. The stated requirements for some graduate programs (example from UC Berkeley) also outright exclude applicants with doctoral degrees. These seem to be saying that holding a higher degree prior to application is a disadvantage (a fatal one in the case of a PhD).

I don't understand why:

• If there are two applicants, Alice and Bob, who have achieved largely similar things, it seems logical that both should have a roughly equal chance of being admitted. However, based on JeffE's answer, if Alice has a Masters degree while Bob does not, it's Bob that gets admitted instead of Alice. JeffE's answer even indicates that if Alice has achieved slightly more than Bob, it's still Bob that gets admitted.

• If graduate admissions is looking for students that are capable of succeeding in its program, then Alice should be more likely to succeed than Bob since she's already had some experience of graduate study. This should be even more the case if Alice already has a PhD - if she can do it once, she should be able to do it again.

JeffE's answer indicates that since Alice has had more opportunities than Bob, she should also be held to higher standard. However it should also be true that Alice has already achieved what Bob has yet to and in fact might not be able to achieve. Further, JeffE's answer seems to be saying that Alice should do the academic equivalent of financial engineering and pass her graduate-level courses & thesis without getting a Masters degree even if she qualifies for it, which sounds silly.

As for applicants with PhD degrees, my first guess would be that this is because multiple PhDs is not a good idea, and the university is acting in the applicant's best interests. However if this is the case, then this is effectively telling the applicant "I know what you want better than you do", which also sounds silly. UC Berkeley's requirements also seem to be saying that if someone with a CV worthy of a tenured position were to apply for a PhD student position, the university will say "no" even though it's clearly better in their best interests (in terms of research output) to say "yes".

Presumably I'm misunderstanding something because if this behavior were irrational, it would already have been changed. What am I missing?