I have a hypothesis that it is the waxes in the tire migrating to the surface in new tires that is causing the squirmy feel.
New tires will have much of this wax on the surface and while the first few miles will scrub that off, it gets replaced by wax that is imbedded in the rubber matrix - it migrates to the surface. This migration diminishes over time so the net effect is that it stabilizes at some low level.
This might explain why the phenomenon appears in both all season and all terrain tires, but is worse in all terrain tires (more rubber to draw the waxes from and the taller rubber is a bit more flexible)
