You'd be surprised at what a good job the individual pieces of Amazon's empire do at operating as individual units as far as competition is concerned. It would be VERY bad business to "screw" an AWS customer because they competed with some other part of the organization as a whole. Given that Amazon operates in so many spaces and could potentially expand to any space, this behavior would effectively make AWS unappealing for a significant portion of customers.
I'd like to believe this, but then I can't buy an Apple TV through Amazon because of some petty dispute over Prime Video (which I really don't care about). So if Amazon the store can pull products to try to protect prime video, then how can I be sure that other units won't?
Well, they claimed they removed non-Amazon devices because they didn't support Prime Video. However, for stuff like Chromecast, the burden lies on the app developer (which would be Amazon) to implement Google's Cast SDKs to provide support.
Because of this, Amazon cannot distribute Google Play Services on their own Android devices and therefor cannot use their own Android devices to cast to a Chromecast. They could enable Prime Video on other Android devices but not their own. They feel this will cause confusion and therefor have decided not to write a Prime Video app for Chromecast. Saying "oh, Amazon just doesn't want to write a Prime Video app for Chromecast", while true, doesn't truly explain the complexities of the situation.
The business decision to remove Chromecasts from the network steps from the above desire to prevent confusion. I personally don't agree with it but I understand it.
That's not the problem. The problem is if Netflix is paying Amazon, then their cost is infrastructure + profit, whereas Amazon only has infrastructure costs.
Fundamentally it means Amazon can be more competitive, and Netflix are hoping they can stay ahead on the user experience curve.
This might be true, but only true until a change in management. Given everything I've seen and read about Netflix, I suspect they have contingency plans and should be able to move to a different infrastructure provider in a few months.
Granted this is true in the case of Amazon, but some conglomerates do not act this way.
Telecom companies regularly try to make rules to ensure those that compete with cash cow voice or cable-TV services have to do so on unfavourable grounds.