Some quick metallurgist answers:
Cold treating is done to reduce the amount of retained austenite in the quenched parts. Retained austenite is bad for dimensional stability and ductility. Under stress it transforms to untempered martensite, which is very hard and brittle. All quenched parts are tempered to give higher ductility. Strength does go down with tempering, but without it the parts would be too brittle, like a file.
REM surface treatment is really just improving the surface finish by removing the peaks. Reducing friction so you have the lubrication film between metal parts and not metal peak to metal peak contact. A set of old worn in gears has basically the same effect, the contact surfaces are polished down. The REM (or whatever name you want to call it) is just providing a head start on this.
My opinion is that these both do provide benefit, but more for reliability than for ultimate hp savings. That's my two Lincoln's worth.