The profile begins and ends in text. That means the psychological properties must be examined in language. This is not what the psyche consists most of, especially the irrational side of the psyche. Simply put: you need to get in a persona head to profiles them on a true psychological level such as Jung. Language is not optimal because body language plays a role. Apparently body and mind are intimately connected. Example: music an stimulate us in different ways. What some may find relaxing another may get depressed. Emotion plays a role. Whether attracted or repulsed. Much like IE.
To get into someone's head you need experience with many people to spot patterns and differences. Jung's system is not a pick which pokemon you are test. rules exist for differences, real differences and distinctions that the mind operates on anyways in the real world. Jung's system is simple but to recognize it you need to become familiar with psyche differences. This is intuitive so any such text doing the same will be inferior because they break things up instead of putting them together.
A test that could work is not really a test but A.I. - In order that lots of data is put together intuitively behavioral rules would substitute preferential language and be raw data, not just speculation. Eventually, by arranging the data in all sorts of angels a more experimental approach is taken to see all possibilities. That is how IBM Watson works. But it does not interact with you, only examines textual language.
Remember that Ni is going to be rather different than Ne or Si. And sample rate is not always going to be enough information. The point is we need a lot more data and put it together to get the big picture when it comes to psyche profiling, especially Jungian descriptions of what the psyche categorizations are. Jungian psychology is a way of mapping things, thinking it is only pokemon is a grim and silly mistake.