If measuring skull shape during the interview process was a) socially acceptable and b) actually predictive of outcomes, why not? The problem is that it is neither. The reason that it is not a) is because it was not b) and thus easily misused to justify stereotypes.
The MBTI is tea leaves reading. It has been experimentally shown to have no relationship to reality and no predictive power time and time again. Even the axis don’t make sense as some are heavily correlated.
The Big 5 is useful but far more complicated. It uses scale and has no pretty little boxes but at least it seems to consistently measure something.
No, just no.
The Big 5 was statistically designed using factor analysis so that its axis are independent. The axis actually came before their description. It’s actual serious research. Psychologists found that some characteristics clustered together and then spent time understanding what these clusters actually measured.
The MBTI however is all over the place. It was designed "using" Jung theory - itself a heap load of garbage - and its axis are total chaos. They even correlate between each others. That’s part of why the distribution of MBTI types is actually so skewed.
Seriously the MBTI is a perfect exemple of what’s wrong with psychology nowadays. On the one hand you have academics trying to do serious research and the other hand you have people motivated by greed pushing random rubbish and gathering a following in the corporate world like a pseudo-cult. It’s both sad and maddening.