Small 4x4s that are best avoided

[Asimo]

Yes I agree that is what happens, and surprisingly easily too.

With an open centre differential the torque you get at the axle with the grip is the same as at the axle where the wheel(s) are spinning, ie not very much. Which is why off roaders have centre locks, and quattros, Imprezas have viscous slip-limiters as well as centre differentials.