Now I don't know how possible it is to design a safe weights workout in those circumstances. There are almost certainly exercises that shouldn't be done quickly, or shouldn't be done tired, or shouldn't be done without perfect form. And almost certainly people are doing those exercises in crossfit gyms quickly, or when tired, or without perfect form, and increasing their risk of injury as a result.
But in a perfect world those people would __still be training that way__, albeit with better instructors and choice of exercises. Because it suits them to train for their sports or general fitness. They're not going to all change their minds one day and become powerlifters.