A little bit of history:
BSF was in regular use before 1910 – I have before me a book from 1907-8 with a table of sizes from 1/4 to 6 inches. Oddly, the 1/4 BSF has 25 tpi – although this may be a typesetting error.
The head sizes for finished bolts and nuts are;
1/4 – 33/64
5/16 – 19/32
3/8 – 45/64 etc.
You might like to compare these sizes with the modern accepted decimal dimensions of Whitworth spanners.
And I suggest that one reason for a large diameter of countersink was because they are intended for use with cheese heads, or fillister, or round, or hexagon heads. It may be that there is a Standard in existence that has not been updated to suit socket head screws. What are commonly called 'Allen Screws' were very rare until about WWII – and are referred to as hexagon socket head cap screws. My understanding of the term 'cap screw' refers to the use of the screw to hold the cylinder head or cap on a steam cylinder.
I'm don't mind anyone raising an objection to my comments, especially if they can add more up to date or accurate facts, but I would be obliged if I could be told of any deletions of my contributions in future. Thanks.
Tim