I recently had this conversation with one of my pro clients.
He's very athletic, has a very good arm (consistently 1.96-2.0 in a game), but knew something was off towards the end of the season.
He thought that he needed to be quicker with his exchange. I agreed, but not for the same reason.
Proper throwing mechanics is a system. A number of moving parts working together to achieve one result. Each action, good or bad, leads to another until the point of release.
His issue, and that of most of the catchers I see, was that his hips were kicking out to his left and his body was turning prematurely.
The exchange took longer to happen because he had turned his upper body to the side, so in order to make the exchange, the hands had to travel further.
The footwork now took longer to complete because in order for his right foot to make its way back to his center of gravity it too had to travel further to catch up to the rest of his body which had kicked out to the left.
This lengthened the path the ball had to take to get into an efficient throwing pattern and caused a delay in shifting his momentum towards his target because his body was already going in the wrong direction.
If I had to pick one thing that can speed up a throw, it would be cleaner/shorter footwork, as our lower body controls the direction of momentum in a throw. However, the sooner the exchange takes place, the sooner I can start my footwork, the sooner I can get rid of the ball.