I think arm circle speed training is generally ineffective, unless combined with speeding up the drive. Here's some cues I find that add speed right out of the box:
-2 Step sequence or other cue to get out quicker with the legs and hands.
-Pull the drag toe into release a little quicker. (Squeeze the knees a little quicker.)
-Use the glove side to pull into release--up together/down together.
You can't speed up the arm without throwing off sequence. Train the whole body to be more efficient for increased speed.
Interesting, because I was just having a discussion about this with someone last night. He is the head coach of the team one of my pitchers plays for, so props right there just for coming out (probably a 45 minute drive) to see what she is learning.
Afterwards he was talking about another pitching coach a couple of his pitchers go to, and what he doesn't like about what she teaches. Apparently it's all drills, drills, drills. According to the HC, the PC says she is trying to perfect each piece of the motion. He and I both agreed that's fine if there is an issue, but it's not the same as throwing full-out pitches and learning to get all the individual pieces to work well together. That's what you're going to do in a game, so you need to practice that way. To me, there is a huge difference between getting one piece of the puzzle right and getting them all to work right together.