I'm sure they would if Netflix was paying - After all Netflix runs on AWS which they have no problem with! :)
In my own personal opinion, Amazon's UX for video is not all that great either, so it would seem both parties have plenty of room to innovate in this space at least, which can only be a good thing. I'm paying a subscription for both, and although I currently use Netflix more, it really wouldn't surprise me if Amazon started rapidly working on their video UX - they've got 'buying stuff' down to a tee, so it'll be interesting to see what they can do with streaming video.