Now if BR▸ had built an East to South chord in Sheffield to allow Woodhead trains to serve Midland station
You mean west to south. There always was a connection from the east into Midland, which is still used today by Worksop and Lincoln trains.
It's easy to be wise after the event but competing rail companies in the 19th century weren't too bothered about operational convenience in the 21st and in the shrinking railway of the 1960s, buying up land in the middle of a city to build a chord line wasn't really an option for BR.
