A lot of the focus here seems to be on the military utility, which is also how I suppose the separation feature was presented in the show.
But an obvious use case would probably have been less dramatic. Anytime two things needed to be done at the same time. Send the drive section to the more distant or dangerous location and keep the saucer where it’s safer, like running supplies or something for a planet.
Don’t know it would have been good TV though?! Perhaps if it was used as a plot device to put the ship in trouble?
It might be big enough to work as a temporary small space station around a planet or just in some general area in need like a fleet in need of repairs and medical aid.