Why is the zonal component of flow in the ocean much larger than the meridional component
It is more of a consistency argument: if a constant-depth ocean with much less relative vorticity than planetary vorticity is to stay that way, the flow must be zonal.  

If there were significant meridional velocities, they would cause significant meridional displacements of water masses, which would then, by conservation of angular momentum, no longer have small relative vorticity. (Same angular momentum and same depth means same absolute vorticity.  Different planetary vorticity then means different [in the opposite direction] relative vorticity. If planetary vorticity was zero before the displacement, it isn't anymore afterward.)