There is the issue of feedback with the headsets as they are omnidirectional. couldn't use them with the accordion- needed a super cardoid mic (Sennheiser 945) that didn't interfere with the condensor mics in the instrument. Same problem can occur with near field monitors. Or hot stage monitors. I usually mute the on board keyboard speakers after having trouble with feedback there too.

As far as singers, watch Tony Bennett (now or then) with a mic. Until recently, he could fill a theatre with his voice without a mic at all!