We might not specifically have time zones, but we'd have something that is equivalent.

We live on an approximately spherical world, its rotation is not tidal locked to its star, its rotational axis is not perpendicular to its orbital plane, we evolved to synchronize our biological rhythms including our sleep/wake cycle to local sunrise and sunset, we occupy a wide range of latitudes and longitudes, and we need to coordinate activities with people who are far away from us.

That puts a lower limit on the complexity of our time keeping system.