I think the coach should call 75% of the pitches but it has to be with conversations with the pitcher and catcher. If they are doing their job, they have scouting reports on the players from year's past and know their tendencies which I don't think a high school pitcher has time to study and learn. I also think the pitch should be called and the next pitch coming in less than 10 seconds. We used a number system where the pitcher and the catcher knew the pitch at the same time and there was no need for signs so it was very efficient. I normally had the pitch called as soon as the previous pitch was caught. But the coach has to have done his job in the past and I seriously doubt by your statements that has happened.
We are in a similar situation. I have been my son's coach the past two years so I called the pitches and we were very efficient. We moved and my son has a great new coach but they are having to get to know each other. They have had to talk about his tendencies and strengths. I think overall it will make him a better pitcher because he is having to communicate about what he likes to do. It will get him ready for college. BTW, I know very few college programs that let their pitchers call their own pitches so it is the norm.