Does this have predictive power? Yes. If I needed somebody to take care of small children, would this test be useful? Yes of course. If I had to pick people blindly for this task, except for the results of this test, then this test would be very useful. Now, MBTI is more sophisticated than this simple test. So to say that it has no predictive power is just silly.
I'm saying that the fact that some people are using it for some purpose doesn't mean that it's actually useful for that purpose.
As for your response, the burden of proof really lies with its proponents - is there any proof of its alleged predictive power?
Without this, I don't think it's reasonable to assume that it is in fact predictive.
For example, the simple test of whether a user clicks a certain link or not already has predicitive power (companies are using this, fruitfully). So a more sophisticated test like MBTI certainly has some predictive power.
Additionally, the added (relative) complexity doesn't imply anything about its qualities.