Purely longitudinal light would kill polarization — which we observe everywhere. Polarized sunglasses work because light oscillates transversely, letting you filter specific orientations. Longitudinal waves (like sound) can't polarize because they only compress/expand along their travel direction.

If light were longitudinal, stellar aberration would still happen (it's about velocity composition, not wave type), but you'd lose the entire electromagnetic spectrum's transverse structure — no radio antenna directionality, no LCD screens, no way to explain why light has two independent polarization states.

The transverse nature isn't assumed; it's measured directly through polarization experiments and predicted by Maxwell's equations, where E and B fields oscillate perpendicular to propagation.