Perhaps It may be more comfortable if you can do the operation on the mobile device, but the other way around can for example my wife Spotify on the FireTV not use when I'm not at home with your smartphone.
It would both app versions are provided, then each can regulate for themselves the Spotify experience individually.
But in the FireTV description of what "they stream on Spotify millions of songs" Write and conceal the fact that one gets an additional need, is not fair.
EDIT: Interestingly, Amazon has now changed the app name in "Spotify Connect" ...
