I agree with the FTC example, but commercial speech and public broadcast speech is a bit of a different realm as well and have their own guidelines. Different constitutional standards.
Coming back to who regulates it, you just answered it. We are going to have the government regulate and define what hate speech is, which I disagree with because in every other country the government has taken these sort of content-based regulation laws and abused the hell out of them. I'd rather live in a country where someone can call me a dirty jew than live in a country when the government is acting as the arbiter of permissive speech.
Also, what is considered slanderous today can be truth tomorrow. At one point, you could be executed for claiming the earth orbited the sun. You would be laughed at and discredited for washing your hands before a surgery.
Another way of looking at it is that one of the protections of the first amendment is that the majority cannot rule the minority with an iron fist. The first amendment allows the less represented voices to speak out. Some of those voices are hateful. But some of those voices are not. If this debate was happening during the civil rights movement, I guarantee that the government would believe that what MLK was doing was considered slanderous and prosecute it as hate speech.