Coach May just preached the gospel. The only real use pitching machines have are to tilt them all the way up and shoot flyballs to outfielders if all the fungo bats break.
Saturday hitting please explain how a pitching machine when fed correctly can create the same timing as live arm? It is impossible to do that and most good hitters I've seen get in there with a machine end up having their front foot going up and down like they are trying to put out a fire because they are trying to time the pitch.
What cracks me up are the guys who go through a pitching motion in order to drop the ball into the machine. Yet when they get to the "release point" it takes them several seconds to get the ball in the chute. It's just not realistic.
As for your example on soft toss and tee work - these are things that should be done although there isn't a live arm. Tee and toss are there to work on the actual swing - not timing. You're only working on part / half of the product (the swing) by doing these types of drills. Hitting off a live arm is there to work on the whole product - timing and the swing mechanics. You don't go to live arm to learn how to hit - that is the final step in the process of learning how to hit. Drills like toss and tees are where you learn to hit.