I think a potential solution would be to delay livestreams by 20 minutes for anyone who isn't doesn't have a direct and established connection (eg following for more than 24 hours) to the broadcaster to give platforms time to censor the worst stuff. Obviously this would make platforms responsible for effective and fast moderation though...
You need to argue that rather than just state it. I can see arguments for and against the proposition, but the facts that Facebook attaches advertising, sometimes removes content, carefully tunes their platform to maximise "engagement", and the user has no direct relationship with the receivers of the live stream, do rather suggest that Facebook is the publisher and the role of the user is more like that of someone who writes a letter to the editor that gets published in a newspaper - except, of course, that Facebook is publishing nearly everything, but I don't see that that's a fundamental difference.
If they're not, why do we sue the TV station rather than the production company of the programme? CBS can yell "don't look at us, we didn't make Game of Thrones".
It's their exception that is looking increasingly absurd.