As per this document: https://developers.google.com/cast/docs/android_sender You need Google Play Services (see https://en.wikipedia.org/wiki/Google_Play_Services#Concerns) to write an Android app with the Cast API.
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.
Fundamentally it means Amazon can be more competitive, and Netflix are hoping they can stay ahead on the user experience curve.
Edit: See jedberg's comment below for where the real money goes.
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.