> I liked to use a Bluetooth headset. What I really want is to pair the headset (or microphone or whatever device) with the dock, not the computer. As a result, switching just didn't work. And Bluetooth is finnicky at the best of times. This was a pain point;

You can resolve this one with those dongle that did the pairing on the dongle itself, e.g. Sennheiser BTD-600/700. The device will appear on the host machine as a non-Bluetooth audio device.