If there were a taekwondo dojang and an iaido dojo--all other factors being equal--it seems to me that the decision would be based on things like interest level in weapons versus empty hand, interest level in one culture or the other, interest in competing, etc. Now, you could argue that all of those things are shaped by personality type. But, really, do you need to understand the personality type that shapes the preference in order to act on the preference? I don't think you do really.
I think personality comes into play more in your approach to learning and performing that style. So take fencing for instance. How you fence (versus whether you fence) might be shaped by personality. Though, again, I don't think it's vital to understand personality type in order to analyze performance.
Interestingly, as well, I've seen personality type vary pretty wildly depending on the activity. I've seen people who are generally shy and inwardly focused suddenly start barking orders and charging the hill in paintball. I've seen similar transformations in the training hall. The way our personality manifests itself in one context can change pretty radically in another.
Stuart