If the gig already has a PA set up, great, this approach is quite viable!
But what if it's a small club that doesn't have a PA? Now the band has to supply the PA. So does the band supply enough PA to handle the bass too, when in reality the PA could handle just vocals if the bass player had a bass rig of his own? If the band-supplied PA has to carry bass as well as vocals, then the PA cabs are now larger and heavier...nothing has been gained.
Take a good PA speaker to play through it, and the singer can sing through it at the same time.
Less to carry.
Cheap PA's that just handle vocals are 95% crap and not good enough for vocals
Powered PA speakers are lightweight these days and a very good value.