Put an average PPL in an average light aircraft in moderate turbulence and watch then slap the controls from side to side (large abrupt aileron movements) trying to keep the wings level.

Makes good sense to recomend that such pilots limit speed to Va in such cases so that the aircraft is not overstressed by over control.

Remember also that the Vn envelope is single axis non-reversed. At a speed below Va, acceleration in more than one axis (pitch and roll for example) or a sudden reversal in loading can overstress. See the AAIB report into the Piper Arrow break-up.

Regards,

DFC