Correlation doesn't guarantee that the mapping preserves meaning. In a group of people there could be a correlation between dietary preference (for example) and personality type, but that doesn't mean that a mapping from one to the other lets you treat the former as a proxy for the latter.

Myers-Briggs is tainted by the idea that there are no bad personalities.

Think of it as a test which outputs a color hue: red, green, blue or some mix of them. However you don't care that much about hue, you mostly care about brightness, but there is no correlation between hue and brightness so you can't see it from the test. What you really would want is a test which outputs red, green and blue brightness, then you can both see the total brightness and if you really want you could also look at the different aspects of it as well. This is what you get from the big 5.