Hmmm...'short final' means 500 ft to me.
Spin recovery means more than 500 ft to me.

Better to maintain approach speed, and recover from a stall if you must,
not a spin.

Very true. But a spin (incipient) -- or any other type of cross-control
stall is more likely to occur during the landing phase. Say you're
approach, for some reason you're already stepping on the rudder, student
pulls to "stretch" the glide. A wing is more likely to drop upon
stalling... (spin) and recovery is a matter of luck. Else, it might turn
into something like a "under the bottom stall". Nasty stuff... Spin
training to me, means "awareness" to such thing. Not necessarily a
guarantee that low altitude cross-control stalls can be recovered without
ending in a "under the bottom stall" or if slipping, in a "over the top
stall" But, if well trained, I believe that with some quick instincts and
luck, recovery may be possible.