Yes exactly. That is the sort of solution people would want. As you say, if a bigot gets an audience in like, the paper, then one of the first questions is "who let this happen?" and then the one responsible is usually disciplined by the paper. Importantly, no paper ever violates the first amendment by doing so. If you tried to make it so the police had to show up and fix it that would put them in the position of violating the first amendment.However if a person were to get an audience being a bigot, I wouldn't believe it to be the governments right to shut them down. Usually those sorts of things take care of themselves though, companies don't like being seen to support racism (or those types of things). Look at Opie and Anthony.
Neither is disciplining threats. The police may show up for those, but it is still not a violation, because your rights are only as protected as the next persons.