It was never clear to me who was preventing this from happening, Apple or Amazon. Since it was available on the iPad, it just did not make sense for it not to be on the AppleTV.
If you go by this crowd around here, anything negative is always the other guys fault... so Amazon was totally in the wrong on this one. They clearly just did not want all the revenue they could make by selling this service to upwards of millions of

TV owners... because, you know, Amazon doesn't aggressively chase dollars. With this, they'd rather just do without... to make some kind of point

or as more popularly spun, to sell their own hardware.

It was Amazon. I sincerely doubt Apple blocked the app from being on the App Store.
Of course, we ignore rumors of Amazon wanting the same discounted deal off Apple's cut (equivalent to the concession that Netflix got) rather than just give so much to Apple right off the top. Why? Because that would imply Apple plays a part in this not happening, and again, it's always got to be the non-Apple entity's fault no matter what.
My suspicions- which are just my own wild speculation- Apple finally decided to cut Amazon a more favorable deal (meaning not demand as much off of the top) and it hit some threshold to motivate Amazon to finally go for it.
If true, the same approach to win:win deals where the non-Apple entities can see enough profit (or non-loss) to go for it too is probably similarly key to the long-rumored Apple subscription service coming to market. I find it hilarious that smaller, much-less-capitalized players can orchestrate streaming service deals while "more-money-than-God" Apple can't get one done. Of course, I know, I know... also not Apple's fault in any way. All the other players just don't want all the revenue that would be made by selling their content through an Apple-branded subscription service to potentially millions of

TV owners... because these players so often tagged as "greedy" in countless threads would rather forgo cash revenue than make the
same kind of deal they've made with many other middleman (streaming distribution) players.
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What I find most interesting about
this rumor is the potential for an

TV (or perhaps just tvOS)
segment. I doubt such a segment would cover just this solitary announcement. So I wonder what else will be rolled out for

TV?