There is nothing simpler or more elementary than the quantum mechanics we already know on that page.
Don't take his word on how quantum mechanics is thought. While we don't teach undergrads it, there is a conceptually simpler approach to quantum mechanics: Feynman's space-time approach. Not only it is conceptually simple and intuitive, it most importantly gives an elementary understanding to the principle of minimal action (sum over all possible paths in space-time) but it also offers a way of calculation that is much better suited to certain class of problems. Now, that is useful.
That is how quantum mechanics is made simple and intuitive (and that is superior pedagogically).
Not by introducing new and strange additional concepts such as negative probabilities as basic things just because you can.
The reason we don't teach path integrals in the undergrad is, we expect students to actually use it for calculations, and unfortunately the mathematics is much more involved in comparison to matrix mechanics or wave equations where you can get away with "basic" maths.
If you have a very good intuition and understanding of quantum mechanics, it is doable though, see Feynman Lectures on Physics Vol. III (not sure how many percentage of the students will actually be able to absorb the intuition along with the new information though).
Don't take his word on how quantum mechanics is thought. While we don't teach undergrads it, there is a conceptually simpler approach to quantum mechanics: Feynman's space-time approach. Not only it is conceptually simple and intuitive, it most importantly gives an elementary understanding to the principle of minimal action (sum over all possible paths in space-time) but it also offers a way of calculation that is much better suited to certain class of problems. Now, that is useful.
If you're a layman, you can read "QED: The Strange Theory of Light and Matter". If you know some physics and maths, you can read: http://www.feynmanlectures.caltech.edu/III_03.html
That is how quantum mechanics is made simple and intuitive (and that is superior pedagogically). Not by introducing new and strange additional concepts such as negative probabilities as basic things just because you can.
The reason we don't teach path integrals in the undergrad is, we expect students to actually use it for calculations, and unfortunately the mathematics is much more involved in comparison to matrix mechanics or wave equations where you can get away with "basic" maths. If you have a very good intuition and understanding of quantum mechanics, it is doable though, see Feynman Lectures on Physics Vol. III (not sure how many percentage of the students will actually be able to absorb the intuition along with the new information though).