My understanding was that Whitworth sized his hexagons so they could be produced reasonably easily from nomial fraction sized round bar stock. Probably by forging or rolling down as machines able to cut round down to size in production quantities were not common when he first promulgated the standards.
The large hexagons of the original Whithworth sizes appear to be derived from some intuitive internal stress assessment based on relative depth of thread and the amount of metal between the thread and the hexagon. Large heads being desirable anyway when bolting timber or not too accurately finished plates and beams together as was very common then.
We tend to forget how much and how rapidly basic stock material size and finish changed between Whitworths day and WW1 or thereabouts. From the viewpoint of the amateur and producers of modestly engineered componets series production WW1 standards are pretty much good enough. Just a lot more expensive (relatively) to achieve then. General state of the art in Whitworths time could be fairly, by todays standards, said to be "Gwad, that's rough, real rough.". The high priced, highly finished "artistic" products of clockmakers et al being totally atypical. We get a distorted view of the quality of things produced in the past because all the ordinary cheap stuff that most folks had to use fell apart and was binned long before the antique and similar buff were born.
clive