Earlier quoted context omitted.
The way to preserve free speech (really "free promotion" or "free publishing" in this case, as there are other avenues for these videos) is exactly what you say — consequences. Newspapers have free speech, but are subject to libel laws, for instance. There's no real mechanism to hold YouTube to account for promoting and spreading this stuff, and they are naturally incentivised for that mechanism never to come about.…
youtubers are also subject to libel (or slander?) laws. the ones with a large audience also make enough money to be worth pursuing in court. newspapers are no more liable than youtubers for merely being incorrect.
The core point is the same: the platforms want to avoid enforced regulation, so they're self-regulating in ways that free-speech proponents don't like