Boost this one to the top, it's the official reason given by sony. You can disparage it if you want, but it has technical merit. The audio codecs supported by mainstream bluetooth devices are meant for music, where you want the highest possible quality and can tolerate a slight delay between when you press play and when the music actually starts.
In video games this means you get a noticable delay on the audio. With classic video file playback like a movie, this can be compensated for by delaying the visuals so thay match up with the audio, but delaying the visuals in a video game is an even worse experience for the player.
Sony's use of a proprietary audio codec via their wireless controllers is pretty justified. They're able to optimize for latency and it shows (or rather, it doesn't, since you probably would never notice it).