I don’t agree.
Here another example with same loading configuration but different thicknesses. (Expanded view of CPS4 elements)
CPS4 elements, 1mm and 1000mm one on top of the other for comparison.
Upper set of Pictures considers CPS4 where Szz, Syz and Sxz are minimized by means of the workaround explained above.
Lower set of Pictures considers CPS4 but with a regular Elastic material definition.
Plain Stress compliant is thickness independent while bottom is not.
VM results deviates considerably.
Bottom could be “comparable” to the z-unrestrained 3D solid element but isn’t “reliable” as a Plane Stress Solution.