Allowing Enchanted weapons to recharge over time, isn't that what the Enchant skill in MW did? If it did then I'd say it'll do it again in Skyrim.
The enchant skill in Morrowind primarily did two things, it affected your ability to crate and recharge enchanted items with soul gems, and reduced the charge cost of using an item, I believe. I don't think it effected how quickly items recharge automatically.
Honestly, though, I don't even like my cast on strike enchantmented weapons having a limited charge at all, because it just doesn't seem right that my magic weapons should have limited ammunition, especially since you still have to worry about them breaking, and for bows, you also need arrows. Obviously, if cast when used enchantments return, these should have limited charge, because as they were in Morrowind, they were basically like spells except they drained the item's own charge instead of your magicka, removing the charge entirely would make them even more overpowered than they already could be. But for weapons, it just seems unnecessary. I use weapons with this kind of enchantment because I want to enhance my attacks from that weapon with magic damage, I don't really want to deal with it suddenly losing that magic damage after a few strikes, other RPGs do fine without giving enchanted weapons limited charges, I see no reason why the Elder Scrolls couldn't.
Regardless, though, if weapons MUST have a limited charge, it should recharge over time, because I too often didn't bother with enchanted weapons in Oblivion, in part due to the need to constantly recharge them manually, though the decision to make it impossible for players to repair enchanted items with an armorer skill below 50 also discouraged me, until I had a high level in that skill. Though players should still be able to recharge enchanted items using soul gems if they so choose in order to get the charge back more quickly. I also think I like the idea of a spell to recharge enchanted item, maybe call it "Recharge magic items" or something, and have it restore the charge of any currntly equipped enchantments by a certain amount determined by the strength of the spell, and these rules should also apply to cast when used items, if they return.
Soul gems should be very rare, but not get used up when discharged.
Wouldn't that kind of make Azura's Star obsolete, seeing as the entire point of it is that it's a soul gem that doesn't dissappear when the soul trapped in it is used?