Why, we have two slots, if you put a weapon in both you can do different damage, with enchanting it would possibly be a huge force multiplier.
Main problem is how du you level it? Simply by equipping two weapons and using one?
If you only have one weapon equipped you level one hand weapons?
Sounds counter intuitive, as a special use dagger with poison or enchantments you rarely use will change how your level. Now add if you remove one weapon to cast restore health or other spells.
My guess is hand to hand, and dual wield is perks for one hands weapons.
I suspect that's the case. As I'm still not convinced hand to hand isn't in, and dual wielding as a skill has the problems you mentioned. And I don't see why dual wielding couldn't be handled as a perk for one handed weapons, seeing as the only weapons you can dual wield are one handed weapons anyway. Equiping different spells in each hand or a spell in one hand and a weapon in the other doesn't count, as that really wouldn't be the same as holding two weapons at all, and I see no reason to penalize it. Sacrificing what other things you could hold in that hand seems enough of a tradeoff to me.
This is, of course, assuming the game doesn't just assume all characters are ambidexterous, with each hand being equally effective, and only your skill in the appropriate weapon modifying your effectiveness with it, thus rendering the entire issue meaningless.