Most FSAE cars use a motorcycle engine, which is transversely mounted (i.e crankshaft axis runs left to right). As this axis is parallel to the rear axle line, there is no need to change the direction of the axis of rotation at any stage. Furthermore, most of the motorcycle engines used in FSAE are normally used in conjunction with a chain final drive - there are sprockets ready machined available off the shelf to fit the output shaft of the gearbox. Hence the simplest way to transmit power to the rear axle is from a chain drive with the sprocket mounted on the diff casing.
Compare this to an F1 engine - the crankshaft runs longitudinally so a bevel gear is needed at some point to allow power transmission between two shafts at 90 degrees to each other.