How does pulling back provide better steering during rollout for light GA planes?
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.