I always found the quality of Amazon Instant Video played via Airplay to be far inferior to the quality available on computer screens, etc. I had attributed it to the video content having to come down wirelessly to my phone then wirelessly back up to the Airport then over the Ethernet to the AppleTV, then found that the AirPlay spec actually doesn't do that (unless Amazon was doing things horribly wrong, they would just send a URL over to the ATV which it would stream from, similar to what Chromecast does). When I switched to the FireTV stick for Amazon content the quality improved dramatically (but the FireTV stick will randomly cut out and complain that the network has been disconnected in the middle of movies, a clear instance of Amazon Quality, so I don't use it much either). So, if we do anything on Amazon Video it is generally something we don't care if it gets interrupted (so no movies or tense shows) or something we can watch on a computer screen (where the Silverlight player replaced the older Flash player and lost several key features, so even that is less likely to happen).
I like the Amazon Prime service. But, expecting me to buy a new Fire TV box after the lemon they call the FireTV Stick is just not realistic. They are letting their other mechanisms of access wither on the vine. At this point, when we decide if we want to pay for Prime shipping again next year, it will just be Prime Shipping that falls into that decision (and as others have noted, it seems less and less reliable and so less valuable, even as they have raised the yearly price).