Our characters should definitely be able to remember what they made, because we obviously arent capable. Yes. Thats the essence of an RPG. Making characters that are smarter then us.
(this is not a joke) :P
I don't agree to your theory. For me, I've got far more important things to remember "in real life" then what can be crafted in a video game. Things like that this I just don't bother with, unless it is absolutely required to solve a puzzle. Other then sharpening melee equipment, I don't plan on using crafting. Now if the requested feature is added, that is a different story

I'm not sure if that requires level 1 or 2 crafting to sharpen a sword on the grinding wheel behind the blacksmith house.