You summed up pretty much the exact problems with MBTI I was thinking myself too.
Not MBTI itself, but the tests. They conflate logic with having autism and feeling with being gay. Plus, they usually assume that F(feeling) means you suck at systems thinking.
So much this. Being an F type somehow means you can't think with logic. Just. No.
Well, these problems are expected when you try to explain subjective interpretations with inductive logic. Jung could see the big picture (but he missed lots of details), but the people who try to create an objective model will ultilmately fail a lot before they're able to do a decent job.