I'd agree on the weak Drain as a training spell, but isn't the Damage version going to lower your max until you heal at the chapel? (or chug a restore potion). ...
No, a damage fatigue effect will damage your current fatigue, not your maximum, and you will regen it back at about 10 per second. I just tested by creating a spell as follows: damage fatigue 3 on self x 1 second. Buffy spammed it continuously with no ill effects. Her fatigue was regenerating faster than she was damaging it. A similar spell using drain fatigue would work just as well and is actually the one Bufy grew up with for training her destruction.
It's just like if you got hit by a damage magicka effect; it drops your current magicka (not your maximum total) and you regen it back. Damage health works the same way, but of course you don't automatically regenerate it back.
It is not like having a primary attribute (like speed or agility) damaged - that is permanent until repaired as you pointed out.