Firefox had a version for Fire TV (which worked on Android TV as well) but they killed it off.
Why Chrome isn't supported is a different beast. Since it'd already running WebView anyway, Chrome would be an easy addition. But Google just expects you to stream from apps, not from a browser (they probably expect you to have a phone to browse or cast from).
Because they don't want you to download contents on Android TV...duh
Use Puffin browser for better navigation
TV Bro is what you want: https://play.google.com/store/apps/details?id=com.phlox.tvwebbrowser