Variations of this have been suggested many times. I'd be curious to try it someday if we could figure out a way to do it that didn't put anything important at risk.
It would make me less likely to upvote more than one comment per thread. That seems like a downside - a good thread can have several comments worthy of upvotes.
A slightly tangential question that I have tried looking for an answer in the FAQs but couldn't: what is the required karma to earn the downvote privilege? Couldn't find this documented anywhere. I apologize if I didn't look hard enough.