Agreed. I'm looking to replace 5 Roku's with Fire TV Stick.
Great question. I am stuck using a wired headset. How can Roku be so far behind the on technology? It's not as if Bluetooth is new. Its been around a while. The way I have to work the headset is to have a shirt on with a pocket so I can put the remote in it because my headset is connected by a cable. The way I see it is if a 66-year-old guy is asking for a feature you do not support, you are definitely way behind the technology curve.
I am also disappointed in Roku with lack of BT support. Amazon Fire has had direct BT connect for years....I bought an Ultra Roku device - supposed to be the Cadillac of Rokus and still cannot connect my Bose BT speakers, it will only support my iPhone and iPad. Amazon Fire connects directly to all the BT devices without any trouble.