Yeah, I understand the chain that causes this, but the root is the same. The advertisers are only upset because of those same bogeyman.
The problem is ultimately those people that care that the word is used, but not why or how.
To me that feels like something society is struggling with lately. People looking for something to belong to, and attaching themselves to groups and causes without fully understanding the cause. Promoting civility is good. Condemning certain words in all contexts is not about civility. It's about proving you belong.
News agencies do not sell clarity and accuracy, they sell advertising views. Enough of the suppliers of advertising views will stop supplying that good for news agencies to sell if they encounter a “fuck”, even in a context where it wouldn't earn an FCC fine, that news agencies have a clear economic incentive to avoid the word.