I can't really say I like the idea of enchantments draining the player's magicka, after all, characters who do not use magic are going to be using enchanted weapons a lot, really, that's pretty much the way to go if you want your weapon to do the highest amount of damage possible, mages actually won't be using magic weapons that much, because they need their hands free for spells, generally speaking, a warrior who does not rely on magic has no need to worry about raising magicka, and can instead focus on other things that are useful to warriors, making enchantments dependent on magicka forces other character types to concern themselves with it as well, or just swear off enchanted weapons, because otherwise, they're going to constantly be running out of magicka. Besides, it kind of seems to defeat the purpose of enchantments entirely, why waste time with a sword that burns people when it hits them when you can just do the same thing with your hands, if the sword draws from the same energy you'd use to do the latter? With the sword, you also have to worry about it possibly breaking as well as its weight, if you just use magic entirely. Finally, it doesn't seem to make much sense, enchantments are supposed to draw from their own energy, or in this case, the soul gem you use for enchanting, the soul provides energy for the enchantment, if the enchantment has to draw power from your own magicka, then it defeats the purpose of using the soul.
Though that does give me an idea, assuming that enchantment charges remain, perhaps using your own magicka could be an option for enchantment recharge, maybe as a perk for enchanting.
What I say they should do is just ditch weapon charges entirely, I see no point to them, no RPG I've played that is not the Elder Scrolls has them, yet those games don't seem to be unbalanced by the fact that your magic sword doesn't have limited ammunition. If cast when used enchantments return, of course, those will need charges, but for weapons that just do damage on strike, weapon charges are really just an unnecessary annoyance. The strength of a soul used in enchanting can instead have the effect of adding another limitation to the strength of the enchantment beyond the enchantment value of an item (Which should also return.) much as the strength of the soul did when creating constant effect enchantments in Morrowind.
If for some reason, Bethesda is just really obssessed with the idea of enchantment charges and just isn't willing to part with them, they should return to Morrowind's method of having them recharge over time, in Oblivion, I often just didn't bother with enchanted weapons at all because it was just too annoying and costly to have to recharge them constantly.
Oblivion's system was fine but how is Soul Trap going to work with Mysticism gone.
Just because mysticism is gone doesn't mean the spells under it can't still exist, it IS possible to change which school a spell falls under between games, after all.