How does pulling back provide better steering during rollout for light GA planes? I had requested clarification on an answer to the question, How do I keep a C172 straight on the centerline during landing/rollout? I did not comprehend how pulling back after touch down provides better steering, the reply to my comment was:

The nose gear won't be off the ground, it will just have less pressure/force on it. The oleo strut won't be compressed, and the wheel will have an easier time turning side-to-side smoothly.

But,

Isn't an uncompressed strut (or lightly compressed) limit/lock the steering because of the nose gear centering cam mating?

AFAIK, at least for cars, better steering happens when the front axle is loaded more, whether mechanically or aerodynamically (front-end downforce).

In jet-liners, pushing forward on the control column after landing (or during takeoff roll till about 80 knots) to firmly stick the nose gear is in many SOPs for better control (type dependent; degree of pushing varies). Boeing 777 example:

On touchdown, take positive action to lower the nose gear to the runway and maintain moderate forward pressure on the control column to assist in directional control.



So what am I missing? I don't presume to know more than the above 3 points, after all suspension engineering is not an easy field (with the big shots working for the big racing teams).
Let's limit the scope to light GA planes (in tricycle configuration, of course).
I'm not questioning the validity of the technique, rather inquiring about the physics involved, perhaps there's more to it than the strut?
Pulling back on the yoke does not improve nosewheel steering.  If there is enough elevator effectiveness to hold the nose off then there will be plenty of rudder authority for directional control.    

Not all airplanes are the same of course, but the Cessna 172 you specifically mentioned has a tendency for the nosewheel to shimmy at high speeds.  Holding the nose off as long as possible reduces the annoying vibration and stress on the nose strut.  It also prevents the pilot from over controlling.  

As the elevator looses effectiveness so too does the rudder, and once the nose falls through direction control is maintained through nosewheel steering.  Ideally this transition is smooth and virtually transparent to the pilot since rudder pedals are used for both.