Regarding MBTI, in my experience the majority of people tend to have strong dispositions and repeatedly test into the same type. I've talked with a few coaches from the Center for Creative Leadership (who do MTBIs across hundreds of people), and their experience is the same.
MTBI is about natural inclinations. For example, testing as an introvert doesn't mean one cannot be an extrovert in certain situations. Many successful introverts learn to be extroverted when they need to. Same for the other attributes.
MBTI is about how you answer the questions posed by the sorting test. Sure, many people are always going to test the same way. And some people will have personalities that would seem to fit the descriptions, but that's largely coincidence. Consider these questions [1]
"You are almost never late for your appointments. YES/NO"
People don't actually measure their promptness or tardiness before answering that question. They just think "yeah I tend to be on time" or "no I'm late a lot."
"It is in your nature to assume responsibility. YES/NO"
Even if you did have a good way to objectively measure assumption of responsibility, no one will actually do it on themselves before answering the question on the test.
Even questions like this:
"After prolonged socializing you feel you need
to get away and be alone. YES/NO"
Not everyone is going to use the same definition of "socializing." I tend to read "socializing" and imagine a party with lots of people I don't know, where there's pressure to perform and impress and get drunk and let loose. On the other hand, some might consider socializing to sit around the house with close friends and family on Sunday afternoon with football on in the background.
MTBI is about natural inclinations. For example, testing as an introvert doesn't mean one cannot be an extrovert in certain situations. Many successful introverts learn to be extroverted when they need to. Same for the other attributes.