Plaguescarred
Hero
Yes i would do this because it's stuff like this that make unique campaign stories! I would even hope she interact with me at some point so it's just not another gem of seeing like all others... 

Why can't they take the eye and then kill the hag, provided that she is not surrounded by townsfolk she gets along with.
As an aside, does this seem like something a hag would actually do?
Depends on the level of players in question. If I was low level, probably, since true sight is really powerful and the other options for it are limited. At high level no, because regenerate is probably close at hand and that stops me from owing anyone.
Personally I'd be on the fence about such an option being given to the players, i assume you've given it some thought, but as others have said, Hags are pretty weak. A situation that arises where the players detect and defeat her turns it into an easy win-win, and sort of reinforces the mindset of solving everything through violence.
Sure. In my experience all you need to get rid of a hag is a divorce and restraining order.