A profanity delay has been used in radio for _much_ longer than that. The first tape delay was introduced by WKAP in 1952. The delay is usually more like 7 seconds, not 20 seconds.
The poor editor is sitting with their finger on the beep button, but a segment surprises them. "Those fuckers <long beep> ..." goes out over the air. It's 5:30 on the drivetime news, prime listening time. The host apologies to the audience and everyone tries to move on.
The general manager calls in, demanding to speak to the editor. Editor is terrified of losing their job. GM asks with as much fury and fire as possible, "Since you didn't have a problem with fucker, i have to know what the hell did they say after that that you decided was sooo much worse you had to beep it out?"
The editor turns bright red, everyone laughs and station pays a small fine. The story gets retold when there's a new audience or a retirement. Guys who tell their version of this story relish the details. even though you see it coming a mile away, almost all of fun comes from those great storytellers.
I've heard people who work in radio describe the Janet Jackson Superbowl incident as a watershed moment. Not only did weeks of meetings and memos about "standards and practices" follow, but to this day it remains a moment in their careers that sticks out as a clear "before/after" point, a "life will never be the same" event."
At first, I thought they were exaggerating and being facetious or joking, but it actually was a major event for everyone in their industry: before the Janet Jackson incident, every radio program at their station broadcast live. If a caller on the air started swearing or saying "obscene" things, they would chide the caller and apologize to the listeners. Now, every program broadcasts with a 20-second delay, and they have a board operator with a "dump button" in case anything "obscene" is said. (As one talk show personality sardonically remarked, "What, are they afraid we're going to start talking about Janet Jackson's nipple?")