The driving forces in new car design are weight reduction, durability, and production costs. Fiberglass is too heavy for the required strength, also too expensive compared to steel. The slow production process and floor space requirements have been alluded to before.
John DeLorean’s car had a stainles steel body, but was expensive for a bread and butter production car. In the mid 50s a British company called Singer produced a family car with an all aluminum body. Again the cost was too high and they went out of business.
Steel (carbon steel) has remained the best option so far for car bodies, although many car components that used to be steel or copper are now extruded plastic, because it can compete with steel in that area.
The only other mass produced economy car I know of that did not have a steel body was the East German Trabant, which had a body made of vegetable-based plastic, the same stuff Henry Ford experimented with in 1945/46, using soybeans as a base. I don’t know the rationale for the Trabant’s body material (probaly local self-sufficiency), but East German economics did not follow the normal accepted practice.
P.S. In the late 50s and early 60s a French company, Panhard, produced a little 2 cylinder front drive car with an aluminum body, called the “Dyna”. It was light and streamlined, and very easy on gas, which was expensive in France at that time. It went out of production for the same reason, cost.