Sounds like you're referring to DMCA where as I was referring to heinous crimes like drug/sex/child trafficking. They do have protection right now in either case.
I'm referring to both. But in both cases, the content hosts don't get punished instantly. They are served with notice of offending content and given a chance to comply. The host and the creator both have avenues of appeal. At least, in the US they do. It varies country to country.