"if eventually you ended up describing the width of a horse's arse"
Two of those has an intrinsic tie-in to the width of a standard gauge rail line. Can you guess why?
Railways use 4'8 because that's what was already in use most places (+- a couple of inches)
Railways originally used the same track width width as horse drawn tramways
Horse drawn tramways used wagon chassis, with standard widths
Wagons were a standard width due to ruts in the road. Noone built to other widths as doing so was to invite broken wheels.
Roads had ruts in them due to centuries of wear, many dating back to the roman empire (when they were better maintained)
Ruts in roman roads were caused by chariots, wagons and other horse drawn traffic.
Roman roads were as wide as they were to allow two way traffic
Wagons tended to be the same width as chariots because chariots defined the width of the roads
Chariots defined the width of the roads as they were military traffic and the roads were military roads.
Roman chariots were built to a standard width to allow interchangability of most parts (and to ensure they would pass freely across the empire.)
That width was defined by rear ends of the two horses operating side by side in front of the chariot.