To clarify the PA28 is no fire breathing warbird on the ground and is very easy to land and maintain directional control. The minor design flaws become apparent: when landing in a crosswind and driving it on in a crab, the nose wheel design has less positive stability as it it aligned with the rudder direction; the bar above the pedals can be pressed resulting in the rudder pedals not being used for steering!
These features are well known and discussed in safety reviews of the type, and should be familiar to most instructors on the type, but sometimes are not.
It is because the nose wheel of the DA20 is not steered directly with the feet
Yes, the DA40 is the same. But with a bit of propwash the rudder works fine at anything above a walking pace.