The problem any content hosting platform has is determining what they should take down for very narrow and solid reasons (like outright copyright infringement). To require them to judge the content will lead them into a no-win situation as they get sued continuously by aggrieved parties who had their content removed. This is not because monitoring would necessarily be targeting one group or another but because major mistakes will be made.
Another problem is the world wide reach of the web. This begs the question of whose laws and mores should be used. This would lead to another set of lawsuits trying to sort out jurisdiction.