As a work around until this is fixed, you could create a .bat with the following commands to close steam big picture mode and then shutdown after a 5 second delay. and add the .bat as a non steam game. (which there are various methods to get around not being able to add a .bat as a non-steam game currently)
cd C:\Program Files (x86)\Steam\
steam.exe steam://close/bigpicture
timeout /t 5 /nobreak
shutdown /s /f /t 0
Nothing extracted yet.
Right now, on a multi-monitor setup, you can set a preferred display to use when starting Big Picture Mode:
It resets to the default display after you exit BPM manually, either via the BPM menu or using the keyboard shortcut ALT+ENTER:
I tested it and it seems to work, even when exiting Steam.
But it seems to not be working when trying to turn off the system:
I'd like to request an option to, say, reset preferred monitor to default before "Turn Off System" or "Restart System".