I think that for this particular answer, it's quite similar to many other ones, where the answerer starts with "I've been doing this in the past", and since many questions bring subjective answers (based on personal experience), I guess it's helpful to have a better idea of what kind of persons submitted this answer. So, as long as the qualifications are directly relevant to the answer, then I see no problem with it.
EDIT: Concerning the fact that junior people might be intimated, it sounds like a reasonable concern, but somehow, not relevant to the particular question you pointed out. Somehow, there are not so many "junior" people (i.e. students, postdocs) who could understand perfectly how an undergraduate committee work, and those who can shouldn't be intimated.
I guess that would be different in a more "scientific" topic. Like, I can imagine that if on cs.SE, if there was a question like "How to do that in Java", and someone would answer with "I've been a Java programmer for the last 20 years, and this is the way to do it", it could intimidate some junior people. But I can't really see the same problem for Academia (or at least, not on this particular question, but I understand that you want to generalize it).
EDIT2: Just to make things clear, my position on this question is that I don't see any problem with people stating their qualifications, as long as it is directly relevant to the question and it's not blatant bragging, even though it can intimidate junior people (I actually think that junior people should not be intimated, in general, even if they're speaking against a Nobel Prize winner). However, I'd be happy to look into any particular case where the qualifications are borderline.