Could it be that the airliner procedures are based on the much higher airflow speeds and having to allow for consequent errors in the OAT measurement?
It's along those lines. The prospect of airframe ice when the indicated air temperature is above zero is mostly due to the pressure-, and therefore temperature-variation over the wing. Where the pressure is low, the temperature is also lower than in the freestream. In aeroplanes with high wing-loading, the pressure coefficients have to be higher, and therefore some parts of the wing surface will be at a much lower temperature than the rest.
A typical heavy jet has a wing loading around 100 pounds per sq ft, while a typical light aircraft has a wing loading around 10 to 20 pounds per sq ft. Hence the effect is much more prominent in heavy jets, and the indicated temperatures at which airframe icing precuations are taken are that much higher. I've never seen airframe icing in a light aircraft with an indicated OAT greater than 1 degC.
While that applies to airframe icing, I can't speak for engine icing, though similar principles may apply. Because of the more serious consequences and rapidly developing timeframe of pitot icing, it seems to make sense to have pitot heat on when in flight.