

Radar would not detect a Styrofoam wall either the return from Styrofoam is extremely low. Radar also can not distinguish elevation differences very well so an overhead road sign can be mistaken for a stopped vehicle or a stopped vehicle mistaken for an overhead road sign.
You’re partially right, stationary objects on the side of the road will have a different Doppler shift than a stationary object in front of the vehicle, items on the side of the road can be filtered. Cheap radars with low sampling rates will not be able to distinguish as their Doppler bins are fairly large.