This is so poorly thought out. I really don't get why some people can't seem to tell the difference between things like MBTIs and astrological signs/zodiacs/horoscopes in terms of their potential to classify people in a meaningful way...
One is an arbitrary mapping of a person's date of birth to an set of traits and prophesies.
The other is a brief summary of a person's personality/behavioral inclinations based on a survey of that person's stated behavior and inclinations. When you say MBTI can be "just as arbitrary," what you're claiming is that it might be true that there is zero correlation between how any individual person of a given personality type answers any of the 93 MBTI questions. Sure, there is variation in people's self-assessments (and personalities for that matter, but let's ignore that for the moment) over time, but it wouldn't be "just as arbitrary" unless it had no correlation at all with basically anything about the person. I find that claim to be completely implausible.
The only way it could be true that it is meaningless is if upon repeated testings, knowing a person's formerly reported MBTI provided no insight at all into what MBTIs are more likely than for the average person in subsequent testings. That's certainly not the case that's been found in the research, so at the very least, it provides insight into what a person thinks that they are like.
Even if it were the case that all the MBTIs are only related to positive traits (which isn't true), the idea that it is meaningless is just nonsense.