It's not that introversion and extroversion "for some reason must correspond to the direction of the primary function". It's that introversion and extroversion are DEFINED BY the direction of the primary function. Introversion and Extroversion in MBTI are NOT to be interpreted by the dictionary definition.
Additionally, Judging in MBTI does not mean that your dominant function is a judging function. It means that your most used extroverted function is a judging function.
So if you have an NT, you ask, "which do they use more, thinking or intuition?". If it's intuition, they are either INTJ or ENTP. Then you ask, "is intuition mainly focused on depth or breadth?". If depth, then they're INTJ; if breadth, then they're ENTP.
Jack's system doesn't work as well -- if you have an NT, you ask, "do they use thinking more or intuition more?". If intuition, then they're NTP (in his system). So far so good. But then how do you determine introversion/extroversion? Instead of being an indicator of something having to do with cognitive functions, it's an unrelated variable -- it specifies nothing about cognition.
Even though introversion/extroversion (the way Jack is using the terms) is a useful personality distinction, it does not accurately correspond to MBTI types. Because of this, some people will have different types in Jack's system and in MBTI. So it seems misleading to even use the same code.
Bottom line, his system, as it is now, contains less information about cognition than MBTI because it doesn't touch on function orientation (although it has added information about dictionary introversion/extroversion). And function orientation is quite a useful piece of data to examine...
So I just don't see why I should give up MBTI for a system that contains less data. If I want the information his system contains about dictionary introversion/extroversion, I could just add it on to MBTI. No need to subtract out useful data.
The problem this fixes can easily be solved by just thinking of introversion/extroversion of functions as spectrums.This leaves the direction of the functions used to be determined by the situation, and by overall preference for introversion or extroversion. This clears up problems that come up with, say, I's using many of the functions in an introverted way (with me, this is Ti, Fi, Ni, even though Fi and Ni are supposed to be way down there in use). It also skips over a lot of the ambiguity involved in determining what use of the function is introverted, and which is extroverted (and don't tell me this is something easy...it may be in the function descriptions, but in practice it is rarely clear).
Jack's mention of this problem is completely warranted, though. The 8 function theory is quite misleading, as Ti and Te are so much more similar than Ti and Ne...what I mean is, there are really only 4 functions -- talking about Ti and Te as separate in the same way as Ti and Fi are separate makes no sense at all.
But PREFERRED orientation of a function is actually quite an easy trend to spot -- people use functions mostly oriented towards one pole or the other; I've never really come across someone that has equal ability with both orientations. And it's also important to touch on the correlation between extroversion of thinking and introversion of feeling (and vice versa, and for perceiving functions). MBTI would be too flat and useless without this stuff.