I can't argue about gamepad support although I would say it is less desktop territory than console/steam machine territory. But for bluetooth support there are definitely good workaround with those usb class compliant soundcards that autoconnect to nearby bt headset/speakers.[1]
[1] I assume you would want to use bluetooth for audio only because anything else usually sucks and can be done better/faster/more reliably with wifi or USB.
[1] I assume you would want to use bluetooth for audio only because anything else usually sucks and can be done better/faster/more reliably with wifi or USB.