It is impossible.
Christoph - it's not impossible. In fact, you've solved it for them: just go and employ about 100'000 mods plus a bit of infrastructure. That sounds very possible for an organization like Google whose turnover is about 90% of the value of NHS annual funding but has less than a tenth of the headcount. If it makes a dent in Google's meagre profits then they might have to change their business model by, say, charging people to post and charging them for hosting. That might also have the benefit of reducing some of the dross and the number of reviewers required.
It's not impossible - it's difficult, expensive and, perhaps, a tad inconvenient, but it's not impossible.
No other industry gets the right to say "We'll choose which laws we obey based on how much it's going to cost us to implement them." Why should Google, FB, etc.?