> I really don't get why sites don't think this way

Because they lose revenue. In Facebook's case because advertisers have demonstrated time and again they won't spend money when their products are associated with controversial content. It doesn't matter how nuanced or obtuse the reason for the controversy.

If you don't moderate what the users post your service becomes a child porn host in a surprisingly short ammount of time is the common fear, and I think its also what generally happens. Though behadings and general gore from shitposters is probably what triggers most censorship programs.

Advertisers hate this approach, unfortunately. This means that if a site is primarily trying to make money, such an idealistic approach will fall to the wayside. Reddit is the most spectacular example of this, moderation by the administrators has in recent years stepped far away from the original approach of leaving up all legal content.

Or you could even let them tag content as inappropriate for those who only want to see fluffy bunnies and have an "give me an unfiltered view" option for everyone else.