Something else less well understood complicates this issue.
Gyroscopic Precession generates a force on spinning objects.
A sudden force on the axis of spin in our case will firstly cause the wheels to suddenly react by their tending to move in towards each other at the leading edge (toe-in). As the axle assembly moves the other way and against the lower rebound spring the opposite forces generate the opposite force so that the wheels then try to toe-out.
Any slight free play in the tie rod bushing will result in sudden ocillation between toe-in and toe-out.
For a motorcyclist the effect is noticed when pushing the handlebar (left or right): the bike lays over to the same side and NOT the other side as you might expect .
Very interesting. I've never considered that at all. Thanks for raising it.