I don't have my D1.4 handy so I can't say much about Fig. 2.1.
As you know, the weld throat is the distance from the root of the weld to the face. The flare bevel groove is shaped such that you can't get the weld down into the actual root, which is the point of tangency between the rod and the plate. That is why the code allows only 40% of the actual groove size for the effective throat ; because that's as far as the weld can reliably penetrate to without changing the shape of the groove.
As far as shop details, it would depend on what your welders are most familiar with. Most often, "simple is best". All you really need to do is show a flare-bevel with no size which automatically means to fill the joint to flush, and that's what you want anyway. The 0.4S takes care of itself.
If you use the S and (E) dimensions, you might want to draw a small detail to show what those really mean, probably in a "General Notes" location. Using either the "S", or the "(E)", or both are technically enough to convey the intent. But I have found that many welders don't remember what all the welding symbols mean. Giving too much information creates questions and delays, or the welding symbol might be misinterpreted and you don't get what you need.
Chet Guilford