This question comes up from time to time: "Why bikes don't have wing mirrors fitted? Surely mirrors would warn of approaching cars?"
In New Zealand bicycles are required to have effective brakes, reflectors and at night, lights. Although mirrors can be useful in some situations, they are no substitute for looking over your shoulder and having a good look around. This also signals to other road users that you are planning to make a turn or change lanes. Mirrors can be useful, but the case for compulsion is weak.