I guess because it switches to a mode that favors latency over sound quality?
I tried using bluetooth headphones on a digital drumkit once, which went about as well as you'd expect. (mind you there was a laptop in between as well)
It somehow works with dedicated USB dongles that are size of a penny. Look at Jabra Evolve 65T. From my perspective as a customer it's an issue with Bluetooth standard, not hardware.
The latency problems are somehow solved when using USB adapters, so why can't we embed those adapters in our devices?
I tried using bluetooth headphones on a digital drumkit once, which went about as well as you'd expect. (mind you there was a laptop in between as well)