I do spend time to pull them apart but not for the reasons of scrap value. I take everything apart so I can keep the washing tub. I'll screw a piece of 1/2" plywood to the tub to cover the hole where the motor goes and the tub becomes a small scrap item storage bin.
Living in a small community, I only get so much scrap so I maximize everything off of it. If I lived in a large area and scrap is abundant, burning through stuff like this would be acceptable. There's no one way to scrap.
I do low volume so I feel I must take just about anything I find. I do gut dishwashers when I find them. There is also wire in the door and silver in the keypad membrane.