Here's the response I got when I inquired via the iOS version of the Amazon Prime Video app's "Contact Support" section (It doesn't say much, but the gist of it seems to be, "Yeah, we're not doing that anytime soon."):
...
I completely agree with your point and I apologize as we are unable to meet your expectations in this case.
I appreciate your inputs regarding this as Customer feedback like yours helps us continue to improve the service we provide, and we're glad you took time to write to us.
However, this is something that we need to take serious consideration for change in how this process works.
To ensure the utmost attention, I’ve forwarded your message to our business team. We're constantly working to improve our digital experience.
I hope as a valuable and responsible customer of amazon you understand our limitations in this case.
Your patience and understanding is greatly appreciated in this matter. We look forward to a very warm and fruitful association with you.
Best regards,
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Amazon Prime has always been one of the best deals on the Internet, but in the last few weeks, I've been taking stock of the "free shipping" for which I originally subscribed (years ago!), and it's starting to look like it's not the great deal it once was. Local stores often match (or beat) the Amazon price now, and the video service (while decent) doesn't offer enough to warrant keeping yet-another-set-top-device in play.
I was planning to keep it after hearing about the Apple TV service, but now that it looks like a no-go, I've decided not to include Prime in the budget next go-round.