I wasn’t thinking they would be responsible for determining legal or illegal. That would be determined by courts and the legal system. For example, libel/slander would require a judgement, not the provider saying they think it’s libel/slander.
It sounds like you're proposing that they have to remove illegal-content, but host legal-content, right?
For example: say someone's advertising a new drug of questionable legality (say, Δ-8-THC). Presumably a hosting-company, unsure of legality, would just take that down for violating their policies -- without necessarily asserting that it's illegal.
But if you're proposing that they can't do that, then presumably they'd be forced into making a clear determination on its legality (as they must host it if legal, and must remove it if not). Right?
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Actually, just to mix crypto in:
Say someone posts a time-locked encrypted-file (a file encrypted such that it'll open after a few hours/days/weeks/months/whatever), and there's reasonable suspicion that it may contain illegal content -- but a hosting-company isn't sure yet, because it was just posted and no one's completed unlocking it yet. Should they be forced to host it?
Now say that an entire community springs up around this: many of the files end up being perfectly legal, while others turn out to be very illegal. How should a hosting-company react?