My solution involves an update to TES lore, but it is also one that will provide an explanation on a few differences between Oblivion and Morrowind's enchanment and magicka systems.
Speculation/Suggestion: Magicka is an ambient energy form generated by all life. Plant-rich regions of Tamriel generate vaster quantities of magicka in higher concentrations. Cyrodill is one such region. Vvardenfell on the other hand is more desolate, and as such magicka is hard to absorb. In fact, you can't absorb magicka in Vvardenfell at all unless you are sleeping. Conversly, in Cyrodill, your body will always be absorbing magicka, without even thinking about it.
Just as casting a spell involves focusing magicka in specific ways, when you bind a soul to an object, you are forcing this soul to constantly focus on generating a spell effect: it's always trying to cast that spell. Instead of using it's own body to generate the spell effect, it uses the body of the wearer of the enchanted object, since that's the closest anolog to it's own body. It also absorbs ambient magicka from the environment, which is easy in areas with high magicka concentration, thus allowing constant spell effects like we see in Oblivion, but when there's not a lot of ambient magicka or when the soul is forced to generate effects when the object causes force on something, as when enchanting weapons, the soul relies on the magicka trapped within soul gems as a source of magicka, like we see in Morrowind. However, some more powerful souls, like Golden Saints or Ascended Sleepers, can still absorb enough ambient magicka to generate a constant effect in Magicka-deprived areas.
There's a limit to how much magicka can be found in a given place, though. If you are wearing loads of enchanted items, they will be stuck fighting for the magicka present in the area around your body, and if they can't get enough, they either won't work or will use your own body as a magicka source. This can manifest in gameplay by placing a "magicka absorption" rating on all enchanted items, and placing an enchantment cap on the player, which varies based on the magicka concentration of the area the player is residing in. When the sum of the active enchanted object's magicka absorption ratings is greater than the area's magicka cap, the player will regenerate less magica. If this cap is exceeded enough that the magicka regenration rate of the player has decreased to 0, then any further decrease will cause the player to lose the exceeded amount in magicka.
Here's a scenario as an example. The player is in an area with only a little bit of foliage. The area's current ambient magicka rating is 13. He has equipped enough enchanted items to get an absorption total of 11. He decides to equip a ring of light that has an absorption rating of 3, and now his magicka regeneration rate has decreased by 1, so it's now only 1 since it was 2 before. He is about to enter a dungeon with magicka rating of only 11, and so when he enters, since his regeneration rate was 2, he no longer regenerates at all, and instead decreases by 1 regularly.
What do you think about this?