There's enough friction on the shaft to slow it down several thousands RPMs in a fraction of a second?
If you answer yes, then I have to wonder how much effort it really takes for the synchros to adjust the speed. I have no doubt that double-clutching would be necessary for a car with dead syncrhos. But synchros can die for reasons other than a lack of double-clutching.
If you answer no, then I'm still wondering why you're not double-clutching on ALL shifts. If the RPM difference is 3k in the negative direction vs. 3k in the positive direction, that's the same amount of work.
EDIT: I had to remind myself of what synchros actually do.
The power comes from the trans input shaft, transfers to a layshaft which is on a plane
next to the input shaft, goes up to the gears which are in constant mesh with complimentary layshaft gears and are
free-floating on the trans output shaft, and then through the output shaft/driveshaft, which is spinning in concert with the differential and wheels.
Synchronizers are connected to and spinning with the output shaft. What they do is connect the output shaft to the gears, layshaft, and input shaft. The load the synchros have to carry is the weight of the gears, layshaft, and input shaft.
When you upshift the synchros must slow the next gear down to the speed of the output shaft, unless you're shifting into overdrive in which case it must speed up the next gear. When you downshift the synchros must speed up the lower-numbered gear to match the output shaft (also the reason you rev-match), unless you're downshifting out of overdrive in which case the synchros must slow down the lower-numbered gear to match the output shaft.
So the synchros are always doing something. Because the gears are free-floating, the entire input shaft/layshaft/gear assembly will eventually come to a stop (barring friction) when the clutch is disengaged
and the transmission is put in neutral. So I suppose the opposite of a double-clutch downshift would be a hold-the-clutch-and-throw-it-in-neutral-and-wait upshift. Good luck timing that though because the trans output shaft is also slowing down with road friction. That's why you hear old dump trucks grinding
upshifts all the time, because it's genuinely difficult to upshift a non-synchro'd transmission.
You can't save all the wear, but you can save about half of it by double-clutching downshifts.