I'm not sure how anonymous figure skating judges really are. Perhaps It is conceivable that some countries use cameras and/or telescopes to covertly record what each judge decides. I'm surprised that no one has done so as part of an exposé.
I bet referees, umpires, etc., in other sports get nasty comments and perhaps death threats too, at least at the highest levels of play, yet they aren't anonymous. It comes with the territory.
One difference is that referees for some sports leagues are full time paid professionals, and are trained by and responsible to a single unaffiliated organization. Ideally, they are unaffiliated with the individual teams, though that isn't universal for inter-league or International play: e.g., in Olympic hockey, the referees come from other countries than the teams.
Making all high level figure skating judges full time professionals, entirely trained by and responsible to an organization that is in turn responsible to the ISU rules committee alone, might help. But that would be expensive. I wonder how much money the International Olympic Committee gets for television rights.
Of course conspiracies could still exist. Besides, there is simply too much emotion, too much subjectivity, and too many variant standards, to eliminate all problems.