You are right that this would be better. But it's not better for them to be known if they are running the Church. And there is an inherent conflict between wanting them to be known and wanting them to be censured and sent packing. Naturally they won't makes themselves known if the result is to be censured and sent packing. They make themselves known when the time is ripe for them to be praised and promoted.
What was it about his Papacy that caused Modernism to flourish and become so public?