If I understand it right, two factors decide thread angle.
One is strength: threads designed to transmit power such as ACME and Buttress etc, have low thread-angles. At the other extreme, high thread-angles ( 80° ) are used on thin pipe where a coarse thread is wanted for speedy assembly and strength isn't essential: electrical conduits and so forth.
The other factor is grip, which is vital in fasteners. Fasteners must be easy to tighten and remove deliberately, but unlikely to come loose by accident. Whitworth, Unified, Metric, BA, and most other threads discussed on the forum are fasteners for which middle of the range thread angles 45 to 60° are suitable. There are many other specialised threads, usually to meet a particular requirement, but also to ensure spares can only be bought from the original maker. Different logic may apply to their design!
Whitworth's thread was optimised for the heavy engineering of his time in Wood, Cast Iron, and Wrought Iron, but technology soon moved on. A few decades later, BA was optimised for light engineering, especially instruments, working in Brass, Steel and alloys.
Whitworth's 55° came from averaging the thread angles of the multitude of home-grown fasteners made by British Industry at the time. Good choice because practical experience had proved 55° was effective. Later threads are a little more scientific. For example, BA thread angles are determined by the pitch which relates to the dimensions of the peaks and valleys applied to smooth out the crude V cut. BA rounds peaks and valleys to a specific formula, and this decides the thread-angle, hence apparent weirdness of 47.5°. The committee didn't start by specifying 47.5°, it's the result of their sums.
Whitworth's thread was a huge success, but not because it's the best of all possible threads. The real advantage was Whitworth nuts and bolts were interchangeable. As already noted Whitworth is unsuitable for light work, but manufacturing cost was also a major issue. Later engineers, notably Seller's in USA, but also the metric crew in Europe, simplified Whitworth by dropping complicated thread rounding and moving to 60°. Seller's and Metric threads are equivalently strong, but easier and cheaper to make. Not so obvious today because threads are rarely lathe cut, but simplified production was a big advantage when they were.
Dave
Edit: I hate smileys!!!
Edited By SillyOldDuffer on 16/11/2021 11:11:38