Would be nice if they did: I am mainly a singer and the reason I started playing other instruments was to know what was going on. Like everyone has said here, singers SHOULD KNOW, but don't, and fragile egos get crushed when a more studious muso asks that person why they don't know the key or chord changes.
Ideally the singer should listen to the band to work on their chops and get better just like anyone else, and playing another instrument, even in another BAND, helps.
Ideally the singer should listen to the band to work on their chops and get better just like anyone else, and playing another instrument, even in another BAND, helps.