I was checking out some info from Kaz on Benching.
He said that with a close grip( 1 finger "in"), you tucked Elbows more and touched lower. This alignment let you use your back and gave you power out of the bottom. After that, it challenged and built up the triceps.
With a medium(28 inches) grip, the bar went sort of straight up and down. Elbows would be "in the middle" or beginning to flare. With this grip you were most powerful in the middle of the range of motion. He said the pecs and shoulders were in the best position to work with this grip. Strong delts would help you most here.
A wide grip (1 finger "out") required you to keep your Elbows out, and touch higher on your chest. This naturally required/allowed you to flare the elbows more at the top. This would challenge/develop your upper chest. And help you refine your "elbow flare."
Kaz said you had to take the bench apart like a puzzle, and work on each piece. So a bench press workout was 3 sets of medium or competition grip.
Then 3 sets of wide grip benches. Kaz even made an effort to do each set of wide benches to a different "high" point on his chest.
Then 3 sets of close grip benches. The idea on the close grips was to keep constant tension on, and stop an inch or 2 off the chest. This was to keep the triceps "in the groove" without having to bother touching low.
He didn't specifically say he used all the different grips to teach him how to use the best elbow position for each phase of the lift. But that was my take-away.