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First--I'd like to hear from _anybody_ teaching HS or general education physics who approaches special relativity from JD's point of view (4D geometry). How does it work?
Last but not least, there is an Occam's Razor argument.
-- Introducing relativistic mass, plus time-dilated clocks, plus
FitzGerald-Lorentz contracted rulers is not a complete description
of relativity. You also need to say something about the breakdown
of simultaneity at a distance. And then you need to worry about
transverse mass versus longitudinal mass versus rest mass. And
so on.
-- In contrast, a modern approach to special relativity is much
simpler. Basically you need to say there are 4 dimensions instead
of 3 (which is trivial), and you need to say that rotations in
the xt plane have a "+" sign in one place where spacelike rotations
would have a "-" sign. That's it. One flipped sign. This gives
you the geometry and trigonometry of spacetime, and essentially
everything else follows from that. I'm not saying you have to derive
everything from simple axioms (although you could). My point is
that Minkowski spacetime is just not very different from Euclidean
space, and this greatly reduces the amount of stuff that needs to
be remembered. By the same token, it reduces the number of ways
that mistakes and so-called "paradoxes" can creep in.