I think this veil of anonymity it what gives users the leeway to bash people on social media, since they can get away with it. Bitter people always have something to complain about and will keep looking for places to project their bitterness. I think it's a great idea to turn off comments when one is perceived as a celebrity or high ranked individual.
It is crazy how bitter people can get on social media just because they can get away with it and this is one of the reasons why we should be part of life private