So with some imagination they could make this a pretty painless process and avoid paying the commission. Which most say is their big problem. They want you to be able to buy from their store without paying commission.
Aside from the reasons Rigby pointed out that this isn't really viable... I don't believe that the commission is the only problem.
I've detailed the reasons I believe Amazon isn't coming to the Apple TV elsewhere... but I'll summarize some of them here as well. It might be too long for you to read... but I really think it explains what is going on right now.
Unlike a subscription service like Netflix and Hulu, Amazon (and Vudu) also sell content. I would imagine that Amazon is far less interested in the yearly "Prime Membership" income, and far more interested in selling and renting movies and TV shows (like iTunes does).
It's the same reason that Vudu and iTunes aren't on the Fire TV. They are direct competitors. Amazon doesn't want you to buy from Walmart or Apple on their device... and Apple likewise doesn't want you to own a Fire TV in the first place. Vudu wants to discourage you from owning either an Apple TV or a Fire TV, because they know they'll always be at a disadvantage on those devices.
Amazon is trying to build more loyal customers (like Apple has), rather than build something that works alongside Apple products. They don't want to cooperate with iTunes... they want to replace it.
Amazon is less interested in making loyal Apple customers happy, and far more interested in building their own base of loyal customers that will use Amazon services, but also pay for their hardware, and purchase lots of content. If that's the ultimate goal, discouraging folks from buying an Apple TV makes sense.
As for the "commission"... while I'm sure Amazon doesn't want to pay it - I think it goes deeper than that. Amazon could easily make a dumbed down app (like the iOS app), but that is basically conceding that iTunes will be the primary option for content purchasing in a home with an Apple TV. Given that they are direct competitors, both for content and set-top boxes, there is no way they'll just concede to being #2 to Apple.
People then ask why the iOS app exists then. The answer is simple: The iOS app is intended for you to have your library that you purchased on Amazon available when you leave the house. Amazon knows that they need to be compatible with an iPhone if they want a chance to compete. 43+% of Americans have iPhones. You can't ignore them and hope to succeed.
Apple TV 4? Current estimates say it only has 13.1% marketshare (all Apple TV models account for 31%) in the set-top box world. The FireTV has a 27.5% marketshare... so Amazon rightly feels that they can really compete with Apple here. If they were to make an Amazon app, the Apple TV 4 would instantly be the only set-top box that can access both Amazon and iTunes. That gives Apple a huge marketable advantage over the Fire TV that Amazon is not interested in giving them.
As for the airplay option... Amazon offered Airplay before this type of competition between the Apple TV and Fire TV really heated up. It's one thing to not create an app that has never existed... and it's quite another to disable a service that you've previously allowed. You think people are mad now about no app? Think about the outrage if Amazon makes it impossible to watch your content on an Apple TV?
All of that to say... Amazon Instant Video and Vudu won't be on an Apple TV any time soon. I'd put money on it - regardless of what their customer service reps tell the public.