For other armor types which are not metallic, like ebony, daedric, dragon armors, I can see why you wouldn't be able to recycle them - those materials are generally not as recyclable as metals, but it's curious you can't recycle the metals.
I guess it might just be because weapon/armor loot is so common that you'd be overflowing with steel, dwarven, and elven ingots if they let you smelt them. Edit: Also, they might be worried about players repeatedly forging, then smelting, then re-forging to power-level their smithing, but that's easily dealt with by having loss-of-material, so that maybe it takes 4 ingots of a particular metal to make a particular weapon or armor, but when you smelt it, you only get back 2 of that type of ingot; also, people powerlevel anyhow, lol.
