Apple is an Apple problem, they usually want a cut of all sales, since Amazon Prime Video offers subscription, pay per view rental, and digital purchase of content it would mean that Amazon would have to pay Apple a share of the proceeds which might be a problem since the margins are already pretty low.
Also last time I've checked Amazon Prime Video works on any device that can accept Chromecasts so this means any Android TV even if it's doesn't have an Android app (I don't know if these even exist) if you have an Android phone, tablet, or laptop can be used to watch the content.
And lastly lets not forget that a Fire TV stick costs 40$....