Stall recovery is absolutely required to be instructed and demonstrated in the private pilot checkride. These are demonstrated to a full aerodynamic stall, not merely to stall warning.

Spin recovery is no longer required to be instructed (and was not previously required to be demonstrated during the practical test either [as many aircraft are placarded as "intentional spins prohibited"]).

CFR for the instruction requirements: https://www.ecfr.gov/current/title-14/chapter-I/subchapter-D...

Airman Certification (Practical Test) Standards: https://www.faa.gov/training_testing/testing/acs/private_air...

Not a pilot either, but it's my understanding that accidental spins almost never happen at altitudes where they're recoverable. Preventing the spin is the only way to avoid most crashes involving spins.

Stalls, on the other hand are part of standard instruction. Recognizing the beginning of a stall early and preventing it will prevent the spin.