Google prohibits Android forks like Fire OS from using their products and services. You can't install the Chromecast app, for example, on a Kindle, therefore, a Kindle owner is unable to set up a new Chromecast without getting a proprietary "Google Android" device, or using Google Chrome, yet another proprietary Google option, to set up the Chromecast. You'll hit similar issues trying to use Amazon devices to interact with other Google hardware like the Google Home.

Amazon stopped selling Google devices because Google won't permit those devices to work with Amazon's devices.

Side note: You'll find "common decency and basic fairness" doesn't exist in the land of corporate business, and neither Google nor Amazon exhibit it.