Big Five And MBTI

There's little research on MBTI available and since Big five is just better there's little reason for it to get any attention in academia. Furthermore, academics in the field heavily push for the Big Five model because they know its better and yet no one seems to know about it, and companies continue to buy MBTI questionnaires because it’s inoffensive

To be comparable MBTI tests would have to be done in certain ways different from how they’re done in online tests to make it more scientific, like simply giving an ‘x’ result when a certain letter is within, say, 40-60% to eliminate one letter off mistypes.

Big Five reproducibility is around 85% (from the study cited in the link you shared), I don’t know why 50% is considered bad at all anyway but with this it is to only going to increase. I can’t point to a specific study because no one would bother to do it properly and give it the same attention as the Big Five, but I think the point right below this is the next best thing and answers pretty much everything
Look up Big Five and MBTI correlations- https://dynomight.net/in-defense-of-myers-briggs.html#in-defense-of-the-mbti [scroll down to see the table and how to interpret it; similar results here- https://psychology.stackexchange.com/questions/13460/what-correlation-research-has-been-done-on-mbti-vs-big5], two of the axes and letters are highly correlated and 2 of the others are moderately well correlated, and this is without the ‘x’ result typing I just described, so MBTI is just a somewhat worse version of Big Five without neuroticism.

And yeah I’m also mostly talking of these based on how they’d perform on a statistical level in a population