Yeah, by 'detect' above I think we've been referring to the end behavior (e.g. what's in the owners manual) of the automated systems, not the raw RF received. Obviously, radar reflectivity itself is not dependent on relative motion of the object compared to the receiver.
It's not a problem of reflectivity, it's a problem of resolution. In order to detect something distinctly from other things (i.e. resolve that thing), you must be able to distinguish its reflected energy from that of other things by separating them along one or more dimension. Range is usually a good discriminator, but there are many things at (nearly) equal range to the radar. Azimuth is typically not great, because azimuth resolution requires a physically wide aperture, and real estate on the bumper is expensive. Doppler is great for moving things because it's easy to design a waveform with a small doppler resolution, and most moving things (cars, bikes, people) don't move at exactly the same speed as other moving things. However, nonmoving things have a very consistent velocity of precisely 0, and there are lots of them. So they can be very hard to resolve, and thus to detect.
