At 11:45 a.m. last Tuesday, the editorial staff of The Washington Post was summoned on short notice to an announcement on the fifth floor of its building to hear something they already knew — that Marcus Brauchli would be leaving after four years as executive editor. After Mr. Brauchli spoke, Katharine Weymouth, the newspaper’s publisher, told employees that he would be replaced by Marty Baron, the editor of The Boston Globe. As the meeting was concluding, Valerie Strauss, a longtime reporter, asked Ms. Weymouth why she was making the change. Ms. Weymouth, perhaps because of employment agreements that limited what...