So you want to take the sandbox aspect of the game and give it an urgent purpose? This would effectively ruin exploration for me which is deeply rooted in going the opposite direction the story points me. No thanks, some of us actually like the largely non-story related world.
Motivation and freedom doesnt have to cancel eachother out, nor should it. Even if a wide open sandbox game is focusing on giving you as much freedom as possible, you should still be given motivation to make decisions.
I never lacked motivation to do stuff in morrowind, but I sure did in Oblivion. It felt completely pointless to run around and discover things, the dungeons had little purpose of cleaning out and a massive amount of quests gave you little to nothing.
When I say pointless I mean that they almost don't help your character to advance forward or become better in anyway, be that by leveling up, earning money, gaining knowledge, gaining friends/reputation or gaining valuable items/weapons/armor.
As much as I love exploring, I still need a reason to do it other than "it's nice to wander around and enjoy the nature". For example, in morrowind I loved to explore, not only because the design of the world was awesome, but because it was thrilling to find new quests, new dungeons or new villages and cities, or if I was lucky, some hidden unique powerful items, deep inside a dungeon or by some hidden and long quest.
In Oblivion I was like that at first, but the more I explored and the more quests I took the less interesting it got, because almost every dungeon was just filled with nothing but wolves and worthless chests. And most quests only have you enough gold to be able to repair the items that got damaged by doing the quests, or maybe I got an item that was worse than what I already had. Just continously collecting ingredients from farms was the most effective way to gain money, and continously beating your horse was the best way to make your character better. And getting the best armor in the game was to simply get to level 20 as fast as possible, and suddenly every NPC in the game is wearing glass and daedric armor and weapons.
I don't like your idea, but I do want it to be more rewarding to do quests and exploring. I'm certain they will not dissapoint me.