I've got a Hornet that came sans the neck shroud. I'm fairly sure this bike was campaigned back in the day and the support tube just under the backbone shows signs (welded area) of having been modified (I theorize) to tighten up the steering angle.
Mark may be correct that this extra gusseting adds some strength to the frame, I dunno but one thing is for sure, it certainly serves to cosmetically clean up the area of the tube welds at the neck. If I ever manage to get this bike back on the road I'll probably run it as is to better monitor that welded area. That being said, I actually acquired a shroud long ago that remains uninstalled. It appears to be from an early version A65 near as I can determine. It's available if you're interested.
The arrow in the first photo indicates the weld on the support tube of the Hornet: