Welding at best is a balancing act of the good versus the bad.
Due consideration must be given to a number of factors and their aggregate influences on the final outcome. With welding, as with many things in life, there are more than one way of achieving acceptable results. The task of the engineer is to optimize the good and minimize the bad influences.
The saving grace in working with the steels included in D1.1 or D1.5 is their weldability is good, i.e., for the most part the carbon content and the carbon equivalency is relatively low, so the preheat temperature is relatively low compared to a higher carbon steel oe a higher carbon alloy steel. Consider the preheat requirement for 4130, 4140, etc. compared to the PH for a steel listed in D1.1 for equivalent thickness ranges.
The low carbon content and the low carbon equivalency of a steel listed in D1.1 or D1.5. Their hardenability is relatively low in comparison with other alloys having high carbon equivalencies. So, if the hardenability is relatively low, we may consider the grain size as being a more critical factor than the Ce if toughness is a concern.
That isn't to say the Ce isn't a concern, it is, and that is just one of the complications considered when the qualification of the welding procedure includes a toughness (at low temperature) requirement. As a result, the applicable code adds restrictions for the thickness range qualified, the electrode classification, heat input (weave vs. stringers), etc. are considered as essential variables.
When impact toughness is an issue, the complexity of developing a WPS becomes much more involved when compared to a WPS for "normal" welding applications.
Best regards - Al