I think I kind of understand what you are saying, like all of a sudden on slippery ice the steering wheel feels sloppy?
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Yes. Btw, do keep in mind that centering is not produce by the caster angle per se. Caster angle plays a role in directing a small portion of cornering force to the steering wheel. When you begin to skid or hit a patch of something that is slippery, the force that is directed to the driver drops
@chunkyazian has that right. As the tire reachs the limit of traction, their self centering force reduces. You can feel that in the steering effort if it isnāt overwhelmed by the power steering. The steering effort goes light, letting the driver know they are at the limit. Works on any surface, dry road, wet road, icy road.
It is a nice early warning that slippery things are going to happen.
Although these days there are safety systems that sense that stuff - Electronic Stability Control - and prevent spins by applying the brakes without your foot on the brake pedal to turn the car into the skid.