That is exactly the point, Amazon's Prime Video subscription service is available on lot of platforms with the 'deliberate exception' of Apple TV.
The comparison of Amazon Prime Video subscription and iTunes is not relevant, because iTunes is a video store where you can buy and rent videos, Prime Video is a subscription service, when I say that I am ignoring the video store marketplace that Amazon has, that marketplace is a separate business. There are things about iTunes service that I don't agree with, but that's not the point I am making.
The validity of my point is limited to the Prime Video 'subscription service', I pay for it and I need Apple TV to be supported because I pay for it.
The closes analog to the Amazon's subscription service is Netflix, and Netflix takes initiative and usually is the first in developing apps for seemingly even the most insignificant platforms. I think Amazon is being stubborn just to be stubborn, there is no plausible reason for it.
If Amazon wants to club the video store and the subscription service together, that's a different problem altogether, seems like they don't agree to Apple's terms for the video store transactions, so one option would be keep the video store service out of the subscription service.