I vaguely remember reading that in his book and was inspired to see if anything has improved since then. My interpretation is "no" nothing has improved on that very specific front since the 60s.
Note that you'll get plenty of replies about completely different question, like "does the math work without spin?" and the answer being "no". And some defeatist commentary (if you've ever heard of the "shut up and calculate" interpretation of QM...)
It intuitively seems to have something to do with symmetry and the finite speed of light and maybe dimensionality and the quantization of angular momentum. I have no intuitive explanation of the peculiar behavior of a spin 1/2 particle as it rotates thru 720 degrees. At least not in three dimensions.
There's been several Nobel prizes for the "what" and "how" and whoever figures out the "why" will likely get a prize someday.
Traditionally in physics new theories require what starts out as weird math at the time. So it'll probably come from automata theory or cryptology theory or whatever rather than yet another real analysis discovery or yet another statistical analysis.
If you want a spooky smoke and mirrors faith to latch on to, I am a big fan of "every form of Math ever invented can eventually be applied to Physics, even if it takes a couple centuries to figure out how". Nothing wrong with having peculiar faith based ideas as long as they don't interfere with life.