No they are not mandatory.
Not mandatory in the U.S. except for the CFI checkride. However, having studied and experienced both sides of the argument, I assert that full down practice autos are mandatory (not in the regulatory sense) in order to become a skilled helicopter pilot. The question then becomes, "In whose helicopter?" My insurance prohibits full down practice autos (with or without an instructor) in my B407, and I am happy that this is the case. However, I have the opportunity to do recurrent training at Bell Training Academy on a regular basis, and there, virtually every auto is to a touchdown (in their helicopter). In the course of 5-6 hours of flying, one is able to do 30-50 touchdown autos under the supervision of instructors who are each doing 3000-5000 of these annually. This concentrated experience makes for rapid progress in improving auto skills. I am strongly in favor, just not in my helicopter!