I have a fire tv and an echo dot In the same room so this makes sense. Only draw back is typically, the fire tv box is close to the TV which is also close to speakers which is playing the sound from the tv which makes Alexa not able to understand what you are saying when far away…
Potential here is using the multiroom audio function, you can have a digital connection (hopefully) which will not rely on Bluetooth which you can not use if using multi room grouping…
Hmmm…I see this being a hit especially since you still have the remote if things are too loud.