Why pull up on the rollout after landing, after the nose wheel is down?
It is a soft field technique but is generally applied on hard surfaces for the sake of the aircraft. There are a few main reasons; 


Take stress of the nose wheel and nose gear assembly which is a bit more fragile than the main gear assembly. This is particularly true in aircraft equipped with a steerable nose wheel like the Cherokee (or in retracts).   
Provide adequate clearance for the propellor. If you look really closely the Cherokee has a low enough clearance such that, excess low pressure on the nose wheel and a sufficiently hard landing can cause a prop strike. This is one of the reasons its so important to check tire pressure in your preflight.  
It also helps to reduce the risk of the fated nose wheel bounce which can collapse the assembly.
Generally it also helps to prevent you from simply releasing the controls after the mains touch down or potentially even pushing forward on the column which would drive the nose down and potentially cause damage. 




During training this also helps to build habits that lead to a good landing attitude and speed bleed off especially if you start out landing flat.