The educational system, as noted by Kersey in PUM, is a tug of war between the SJ and the NF. Presently we're in the NF swing of the cycle.
If you are referring to the tug-of-war between the conservatives and the liberals, then I can see what you're on about. But you're not likely to see an SJ going out looking for fights for dominance. Too much willingness to toe the line, accept the will of authority, and accept the status quo.
Not that people haven't tried. "Gifted and Talented" is one such, but ends up being a mob scene of S types predominantly who want the best for their kids, and are run by intuitives. We have one locally, a probable INFP principle and her (again probable) ESFP or ISFP husband teacher. The S mommies mob the place. I think having N in the inferior makes it irresistible. In practice it ends up being a prep school, with little gifted or talented to recommend it (the terms are terrible too).
Yes and no. We have the same situation here. But the "mommies" are endlessly creative in how to get their kids into a better school, so much, that you'd laugh if I called them Sensors. They are also very, very pushy, way more pushy than you'd ever expect of a P, and way more pushy on a regular basis. They're always strategising as well. It really smacks of INxJ-ness.
SJs respect authority, and respect practical limitations. They distrust change. But they accept that systems aren't perfect, and tend to be more mistrustful of the unknown, and so are apt to accept the status quo. So they aren't a problem.
It is incredibly difficult to deal with introverted intuitives in this scope, because they don't trust the status quo, don't trust in direct evidence, and don't trust others. They'll read a study that says that people who listen to Mozart have smarter kids, and burn all your rock albums, just so that you don't have anything else to listen to other than Mozart. They often don't remember that when you only had Mozart or nothing, you chose nothing, because that would mean that their clever and more efficient intuitions weren't all that clever or efficient after all.
At least rudimentary MBTI is generally know in the system, the difficulties are as you mention (money, etc), mainly it's a quasi-governmental organization which has three major players; the administration, the parents and the industry (textbook producers). Reform is difficult because these three are locked, and given the governmental involvement innovation is nearly impossible.
Someone has to work out the logistics, while still keeping up with existing educational requirements, i.e. a national curriculum (everyone is graded by the same exams/coursework), feminism (women do really badly at exam-graded qualifications, and really well when the entire grade is 100% coursework), practical issues of geographical availability of schools, teachers, classes and children, and those who want to use MBTI as a weapon (My son is an INTJ. INTJs are smart and work hard. My INTJ son should get a good place at university. Your son is an INTP. He lives in the clouds and is lazy. Your INTP son is only good for pumping gas. Any school resources should be prioritised for my INTJ son over your INTP son).
Besides, it will only help, if we are talking about types of people, and not types of self-perceptions, which is all MBTI amounts to at the moment. Sure, we can give them all mental puzzles, and figure out objectively, which ones are which, by the style of thinking they demonstrate. But then many of the NTs and NFs here will turn out to be STJs and SFJs, and many of the SJs and SPs will turn out to be NTs and NFs.
Anyhow, for my kid the education should be on letting him run with the concepts, without having to grind through exercises (but with an emphasis that he does have to learn how to do them adequately. Then his PE class would ideally probably spank him into actually exercising. All administered and monitored by a computer system, which would ensure that he and the ESTJ next to him (who gets lots of memorization, rules to follow and exercises) have equivalent education.
Actually, my maths teacher brought out the best in me, by making us do lots and lots of exercises proving as much as possible from first principles. His intent was that by the time we came to the exams, we'd have answered so many different types of exam questions, that we would easily be able to do well, and by learning to prove things from first principles, it meant that we'd always have a way to solve the problem, even if we forgot the standard methods. It worked. We did extremely well in our exams.
It also meant that when it came to answering questions on maths, my Ne had been developed extremely well, and my Ti was trained to be able to solve problems solidly, where there was no proof. I really had a Ti-Ne framework that I could manipulate at will, and was easily capable of producing extremely solid answers.
I've found a similar process going on with me when it comes to IT. First, I learn the basics. Then I play, screw up, screw up, screw up, until I learn 20 screw ups. Then I know what things make it go wrong, and then I know just what to do to make things work.
I am, at this moment, inclined to think that this learning process is extremely useful to Ti-Ne.