It's really not necessary. Sure, occasionally I run across some edits and I want to throw upvotes at the screen, but that is quite a rare occasion at that. You've already mentioned why we shouldn't have downvoting on them, so I'll skip that.
Why can't we offer reputation?
Editing is meant to improve the post. Edits made on non-community-wiki posts are not meant to actually change the content of the post, but just to make the post more readable and more understandable. Fixing it up to be more useful is the goal here. The vast majority of the time, you're not actually introducing new content to the post, and the vast majority of the time an edit doesn't deserve reputation (those under 2,000 are granted the +2 to help them gain editing privileges). This is a community-driven site; those who care about the content will pitch in because they want to make the site better.
What about comment-style voting?
Adding comment-style upvotes to edits doesn't achieve anything. You can't order edits by popularity of votes because edits need to be sorted chronologically in order for them to make any sense. Each edit is directly correlated to the edit previous to it. This is not always the case with comments, where certain key comments can be upvoted above the rest and still make sense without the previous context behind them. They'd just be random votes on edits.
I'm all for encouraging people to make good edits, but useless votes that they likely won't ever look at doesn't seem like the correct route.
Would it be visible?
Not a lot of people look at the edit history anyways. Unless you have a specific reason to look, chances are you won't. This would likely end up being some hidden feature behind the scenes that a lot of people won't use.