It's not global, but in the mean time you could use a command triggered on profile unload to do this.
Add the "Change Default Audio Devices" action("Other >", "Advanced ⯈", "Change Default Audio Devices") to a command with the desired device selected, then set it to run on profile unload(
, "Profile Exec" tab, check "Execute a command each time this profile is unloaded" and select the previously created command in the dropdown).