Not so fast there. First of all, if we can get rid of false advertising we can get rid of fake news. As a matter of fact, we were largely rid of it during the times of the Fairness Doctrine. Second, and importantly, there are people using the public airwaves to promote fake news. They’ve gotten by with it in a big part by presenting it as partly opinion and partly fact.
You’ll often see a pundit say, “Since X is true, we should do Y” and this is when X is a completely made up thing. “Since thousands of ISIS members are pouring over the Rio Grande disguised as Mexicans, we should build a wall.” My contention is that since X is presented as a fact on a channel that purports to be a news channel, it is being presented as news. Since it’s being presented as news, it is subject to the FCC rule against deliberately misleading the public about news. This is in cases where a reasonable person would know that it’s made up but the audience is made of people who aren’t sophisticated and who trust the source.