Probably a mixture of both reasons on the E-type. The Series 1.5/2 had the US compliant interior as well as the lights rearranged and the engine uglified (S2), so it may have been part of that general upgrade. My guess for the pre1.5s having no plexi is the usual vaguaries/chaos of production. They probably had some new 1.5 bonnet shells hanging around while they were still building S1s, so on they went.
Not sure what drove the plexi change across all cars, either. All I can tell is that several cars seemed to have lost their covers around the same time. Since this would have been an easy change on something like a Duetto, it probably was US market only until the change was standardised on the next series.
Not sure whether the regulation specified height, glare inducement, standard headlight sizes (round, in 2 sizes...) etc etc? The US had (and has) some pretty strange Auto regulations.
I have a Jaguar-nut and general car-freak friend who also worked for some time at Hella...I'll interrogate him on this