Shitting disrespectfully all over news articles where someone died, or ranting your opinions about illegal immigration in every news article that includes a Hispanic-sounding name, or spewing profanity and threats at anyone who doesn't agree with you, is not free speech. It's just being a douchebag troll.
These media outlets have been incredibly generous in providing their private space for public comments and, unfortunately, much of that has been abused by idiots who wouldn't know the 1st amendment from a hole in their own head.
All the things you listed are free speech, and people being douchebags. You are right that many of the comments would turn into if not start out as shit posts, but those shit posts are free speech. The private firm shutting them down does not break any laws, because its their property. Only the government is not allowed to limit speech.