Yes, in general you should be rested and not exhausted after short or at least long rest. It doesn't feel right to me to be exhausted after a rest.
I don't like the multi-stage exhaustion model. There was something similar in the predecessors, but it only referred to the level deprivation of vampires and shadows that needed Greater Restoration spells to be healed.
But IMO exhaustion and level/skill deprivation should be handled differently.
