Answering your question took quite a bit of work. The text below is a summary.
We have been in the “denial” phase for quite some time. My favorite example is Calculus. Calculus courses teach the original development of Calculus, using Leibnitz notation, using pre-1800s development and proofs. The idea seems to be that students should understand Calculus from the ground up, and therefore believe in their final results.
Only one problem: mathematicians in the 1800s thoroughly proved that the original derivations were invalid, and historians of the late 20th century have strong demonstrations that the derivations were bogus. Today’s usual summary of the early days of Calculus is that it was accepted because it gave testable solutions to long standing problems, not because its derivation was convincing. Fortunately, mathematicians of the late 1900s were able to develop a theoretical basis for Calculus (and for set theory also, another major foundation failure found about 1900).
So, in short, students spend their time learning bogus proofs that convinced very few back when they were new, and are not even told why they are doing so, or the holes in theory that each proof was originally intended to plug. That’s a bit worse than a waste of time.
The current situation is also much like the Tripos exam that C.P. Snow complained about. The examination was continued as long as it was because top scoring students were given secure academic appointments. The easiest way to quell complaints about fairness was, at the time, to give the same test to all applicants over both space and time, to follow tradition. Much the same is true for Calculus I today. It is a gateway course, and changing it will bring accusation from whomever fails the final exam. Political complaints have taken very seriously since the 1960s.
So: A crisis is building, but it is not here yet.
For something like Mathematica to succeed as a tutorial in elementary mathematics, it would have to be linked to a believable derivation of the theory it relies upon. That was attempted, for example, by K.D. Stroyan, who is currently offering his course under the Creative Commons license, Calculus: The Language of Change, University of Iowa, apparently current. I can’t evaluate that book, but back in 1993 he has abandoned the 1700s theory and was using 1900s theory.
In summary, much of mathematics education demonstrably does not make sense, as it does not incorporate theory agreed to be valid, or, for non-mathematicians, any theory at all. People with STEM careers are being worked hard enough to inhibit family formation and stability, which makes the industrial system that relies on STEM workers unstable over, say, three generations (~60 years). You would think that improved education and cognitive aids would be readily salable, but so far the educational and governmental organizations appear to be in the “denial” phase.
So, what does it take to break denial? Arguably, Newton’s work was possible because the English Civil War had introduced major changes to English society at about the time of his birth. The Tripos changes that Snowden mentioned came about right after another large change, the Napoleonic Wars and the start of the Industrial Revolution (c.a. 1800). It may be that something of comparable magnitude will be necessary to change the current educational status quo. However, there is also a great increase in home schooling, tutoring, and on-line education. That’s a start, and, should something discredit the educational establishment, I would expect all of those increasing activities to become very widely adopted, and very quickly (several years).
As for CAI threatening teachers:
Speaking from my own experience, much of mathematics teaching appears to be, ah, close to fraudulent to the student. It is ideal for a student who wants to disregard theory and learn to solve standard examination questions, but such a student encounters trouble when trying to solve non-examination problems. Understanding the distinction between easy and difficult problems, between what is known and what is not known, requires either years of work or a knowledgeable teacher. A curriculum helps, but you’d need more than IBM’s Watson to tell the student that there are limits to knowledge and how to recognize them, and then how to try to cross them.
If the teacher does not know that, then the mathematics will be of very use to the student only in solving problems that somebody else has selected and prepared. If the teacher does know that, and the CAI does not present mathematics as eternally unalterable rules, than I'd guess that the teacher could actually rely on CAI for job security.