In theory, yes. But reality is different, especially with an app that cannot make use of the system-level media player that most every other streaming app can. In those cases, there are myriad caveats about how the hardware video decoder treats things differently across platforms. (For a real-world case study: how the TS4K's first major firmware update messed up hardware video decoding, and took about a year to fix; and how about how the Fire TV couldn't handle interlaced H.264 content for years, which had many UK/EU users up in arms.)
Also, being a TV focused app, Channels also has to deal with how different custom versions of Android are treating different remote buttons in myriad ways. Support for the "Live" button on the TS4K is spotty at best, because it is not exposed as a standard button, but something TiVo has cooked up to sidestep the Android APIs.
On top of all of this confusion, Google is constantly changing their "Android TV" platform—or is it Google TV now? No wait, that was 10 years ago …—depending upon their whim. And Amazon's fork of Android is often years behind the base APIs that get updated annually, meaning the ability to use newer and better APIs is out for that chunk of devices.
So yes, it would be nice if everything was equally supported. But Apple devices share a single consistent API, as opposed to the mess that developing on—and worse, supporting—Android entails.