Personally, I don't think Rivera is the problem. He is what he is, a player motivator. Ron is good at what he does. He can relate to players and push them to get the best results out of them. He is also very knowledgeable about defense.
Rivera is not great at calling plays or making personnel decisions. He must be paired with strong coordinators and a hands on GM. Shula was kept around for continuity and saying that his track record is piss-poor is an understatement. He should have been let go last off-season, but our miracle run to the playoffs delayed that departure.
Shula can not be the offensive coordinator next year of this teams wants success. His entire mindset is antiquated. The NFL has been tailored to score more points. Rules now favor the high-scoring, high-flying offenses. The ball-control / good fundamentals approach will not win in this league anymore.