Why is it disadvantageous in graduate admissions to have a higher degree?

Berkeley offers the following rationale for their policy:

The Graduate Council views academic degrees as evidence of broad research training, not as vocational training certificates; therefore, applicants who already have academic graduate degrees should be able to take up new subject matter on a serious level without undertaking a graduate program, unless the fields are completely dissimilar.

Although this is rather vague, it does suggest that they believe that when one already has a PhD, it is pointless to enter another graduate program in a similar field, as one has already demonstrated "broad research training" and shouldn't need more. And since PhD program spaces are a limited resource, and involve a considerable investment of faculty time and university resources, they don't want to spend it in ways that they consider pointless.

That's my interpretation, anyway.

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.

Not at all. PhD admission is primarily based on potential for future success as an independent researcher. Between two people with identical research portfolios, it is natural to judge the person who built their portfolio faster and with fewer opportunities to have stronger potential for future success.

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.

You've moved the goalposts. If Alice produces more concrete evidence of research potential than Bob as a result of her graduate study, then she meets the higher standard expected of applicants with graduate-school experience! On the other hand, if Alice does not produce more concrete evidence of research potential than Bob, despite her experience of graduate study, then Bob is a more attractive candidate.

Merely having been a graduate student is not by itself evidence of research potential; research rarely resembles coursework.

Whether it is made explicit or not, I would imagine that most graduate programs try to evaluate candidates on the basis of future potential. Probably most programs should be more clear about this.

So, for example, if one has been allowed to take qualifying exams endlessly, for 20 years or so, and eventually passes all of them... what does it mean?

It's like age or weight classes in various sports. The possible fact that a 30-year-old can bat 1000 in T-ball aimed at 5-year olds does not earn a spot on a major-league team in the U.S.

Although there's very little age-ism practiced in the U.S. in PhD admissions in mathematics... the point is not "maxing out on prelim exams", or anything similar. It is infinitely more about people on an upward trajectory...