Putting in any avionics that is not listed on the TCDS, which these days is
virtually all avionics, requires a 337.

This is certainly true in practice, but adding avionics doesn't seem to me to
fit any of the definitions of major alterations given in Part 43 Appendix A.
I once asked an FAA avionics inspector about this, and he just said something
about it being critical to safety and thus it makes sense to require a 337.
Does anyone know of a case in which someone has tried to challenge the FAA's
interpretation of this?