The announced product-removal is means to the end of making the service available everywhere.
How so? The new Apple TV supports third-party apps. As far as I know, there's nothing stopping Amazon from taking their existing iOS app, turning off a few small bits of code (status bar updates, for example), and shipping it as a tvOS app, available on the new Apple TV by the first day that it arrives in customers' hands.
There is nothing magical or exceedingly hard about Amazon Prime Video. My 2008 Sony can play it. If Google and Apple aren't offering it, it is because they don't want to, not because they can not.
Yes and no. Supporting additional content providers adds complexity that often results in a less reliable product. That's why Blu-Ray players that support all those content providers tend to have more bugs and be less usable than the simple, dumb players. The whole point of opening up Apple TV to third-party app developers is so that all of those companies like Amazon can create their own apps, so that they, not Apple, are responsible for debugging support for their particular service. If history is any indication, in a few releases, Apple will drop support for Hulu and Netflix and will require those companies to provide their own apps, too, just like they did with Google Maps.
The difference is that when they do that, Hulu and Netflix will have an app out within a week, because they already have working iOS apps that don't suck, and it usually requires only minimal effort to add tvOS support to an existing iOS app (unless you depend on features that tvOS lacks). By contrast, Amazon isn't making their app available on tvOS. This isn't surprising. After all, Amazon also deliberately disabled support for mirroring their instant video app on Apple TV even from iOS devices, and for many years, didn't even allow you to watch Amazon Instant Video over cellular, much less do offline viewing, reserving those features exclusively for use on Amazon-branded hardware.
To me, it looks like Amazon is playing dirty, deliberately creating a substandard user experience on iOS in a naïve attempt at coercing Prime streaming users to buy Amazon-branded hardware. I'm not sure whether they are really so clueless that they don't recognize the importance of the iOS market, or are just so crazy that they honestly believe people will drop their Apple products in favor of Amazon products rather than just dropping Amazon Prime for Netflix. Either explanation leads me to seriously question whether the Amazon management's heads are screwed on straight. Jeff Bezos needs to seriously reorg that entire part of the company, and bring in people who actually have the spine to create a great product that stands on its own, rather than bowing to pressure from other parts of the organization to sabotage their own product in a misguided attempt to use the poor experience as a stick with which to beat their customers into submission.
Want iOS users to actually switch to Amazon products? Create a first-class user experience with the Amazon app on iOS so that users will see it and think, "Wow. Amazon writes great software. I wonder if their tablets are just as good." By doing the opposite, you pretty much guarantee that no iOS user will ever take your products seriously, including your streaming service.
Then again, for Amazon, this is nothing new. At last check, KF8 flowing books (Kindle books with actual support for CSS) still don't work on iOS devices after how many years? It seems like Amazon does its best to make their iOS experience as subpar as humanly possible. So when it comes to them pitching a fit and refusing to create an app for tvOS, let me be the first to say, "Don't let the door hit you in the a** on the way out."
Good riddance to bad rubbish.