It would be inefficient to continuously check for the bit and disable it, right?
I feel there has to be some sort of killswitch. A universal audio control could be very beneficial to users.
The way the current Arduboy2 library and the various sound libraries are set up already caters for this if the developer of the game respects the sound setting stored in the EEPROM. If you are finding games that do not honour this setting then you are better off complaining to the developer (or simply not playing their game!)
Doesn’t your approach assume the developer is using your library?