I first became interested in Meyers Briggs because there was a particular person that I did not understand. He was an individual that I hired and worked for me. It was early in my career when I was beginning to manage people. There was conflict between the two of us. I knew he was a strong performer and yet there was this dysfunctional dynamic that existed which not only impacted the relationship between the two of us but the broader dynamic of the group I was responsible for leading. I knew I was screwing up. I had always approached conflict in one manner. I tried to put myself in the shoes of the other person. In this particular case, it didn't work. I simply could not understand where the guy was coming from and it led to a great deal of misunderstanding.
So, it was after some personal pain that I discovered typology. It was a revelation, because I was able to understand just how differently people could think. I never did figure out exactly what his type was, though I had some guesses. It was enough though for me to guess how he may approach things and that this approach was different than mine. @Mane describes a story where he had difficulty understanding someone - it was a stimulant for him being interested in the topic. In his case, it was a romantic relationship but at the core, it was a similar motivation.
Now to the topic at hand. There are many ways to look at typology. One way is to use it to understand unconscious tendencies. This is useful in my opinion to the extent that it has practical application. So, I believe the primary value of typology is to help understand people, including yourself. Devoid of that practical application, it is interesting but not particularly helpful. Realize I am not saying it is necessarily a predictor of behavior but it does help you to understand how people think and that by itself is a very worthwhile thing.