Sidepulls returned to fashion, in the late '60s, early '70s, long before the concern for aerodynamics in the mid-'80s. In fact, the quest for aerodynamics in the '80s briefly revived centerpull technology through a mechanical linkage in the heavy, complex, and difficult-to-modulate Campagnolo delta brake.
One clear advantage of sidepulls was in removing the flexible cable stop hanger from the system. Raleigh half-solved this problem by brazing a bridge between the chainstays, but that left the front still susceptible to some very non-linear pull under hard braking. The hanger would absorb cable pull with increasing resistance like a spring.