esperent's comment that I originally replied to not only claims that personality is malleable (I completely agree), but that MBTI theory claims that is not. That represents a fundamental misunderstanding of what the theory is claiming.
> How malleable, under which circumstances, malleable to what, which aspects, etc. are all still open questions
Indeed. And the MBTI theory makes a specific and very interesting claim about this open question: that what is malleable, under which circumstances, etc varies between people. And furthermore, that there is an extent to which that variation follows certain set patterns (possibly as a strong statistical average with exceptions rather than a sure thing), such that we can classify people by which pattern(s) of malleability they follow.
This doesn't mean that all malleability is subject to these patterns. There can still be aspects that are common to all people, and aspects that are completely individual. But the claim is that there also some aspects that apply to group of peoples.
Of course, such a claim needs to be substantiated and the current evidence is mostly from clinical observation rather than scientific experimentation. But whether it is true or not there is good reason to believe that the lack of scientific evidence stems from a lack of ability to measure accurately because (as you say) mainstream psychology has very little to say on this topic at the moment and exactly how this aspect of the mind works is still considered an open question.
> That is to say, measuring personality and categorizing people based on personality traits brings us no closer in understanding human behavior. That is to say, measuring personalities and ascribing traits is not only harmful—like GP says—but also bad psychology.
I should note that the MBTI does NOT measure external traits. It (attempts to) measure an actual functional mechanism in the mind/brain (which it postulates to exist).