Nothing happening to iHeart has any affect on CBS. All of their stations are completely paid off with no debt. That's a very different problem.
And as I said, CBS is not "bailing" on anything. They're looking for shareholder value.
Using your logic, and considering the losses Viacom and Disney are experiencing due to cord cutting, CBS would be best to sell TV too.
There is no such thing as a safe business.
An iHeart collapse will be felt industry wide. And deep. And if all their debts were publicly audited, it would be a pretty bad number.
CBS and their other holdings would probably not want to be associated even indirectly with a long-term mess like that - especially if they want someone else to buy their stations.
But seeing as they announced selling off their radio division a week after the iHeartMedia revelation, don't tell me it didn't make enough of a wave to make CBS do this. They could have waited for a year, maybe two. Or even a few months. They chose now.
Of course they're looking for "shareholder value" (aren't they all?) But probably for different reasons than you might think.