You probably should have asked whether they still do them "live live" or "live on tape."
I would suspect most do them live on tape, like this:
As
@Theater of My Mind said, hearing contestants on-air was meant to create excitement and entertainment. But having truly live callers also meant the risk of listeners calling into, say, KIIS-FM, and when asked "Who's your favorite music station?!", hearing them shout "KPWR!" To that add listeners who drop constant F-bombs, who sound like they're on quaaludes, who think the station's transmitter is sending secret signals to the KGB, and who lock up like Windows 95 the second they know everyone can hear them. Prerecording callers "live to tape" lets jocks circumvent all that. If the "first" caller #20 doesn't work out, they can dump the call, answer another 19 lines, and congratulate the "next" caller #20. (Notice how the talent in the video above didn't answer the remaining lines to dismiss everybody still on hold until he was certain the "first" caller #20 had worked out perfectly.)