As I started to think and respond here, I felt like I was about to write a book. . .so I'll refrain and try to be as succinct as possible.
First, my son has been a pitcher and position player and now only a college position player and as a position player it's the mental side of the game that I encourage him to work on during the games. Since position players cannot control what's going on during games, whether it's fielding or hitting, my son and I find it's a poor time to try and work on anything like mechanics. And more specifically, one of the things I encourage my son to do on the mental side is to try and keep thoughts about mechanics out of his head during a game. . . .especially when at the plate. Unfortunately, many coaches put such thing into his head during a game, which almost always doesn't really help during a game. So I have him work on ignoring outside inputs during games, trusting the skill he's developed and taking mental notes and taking those notes to his workouts between games and/or during pre-game warm-ups. And as for summer league, I encourage him to relax and experiment with situational approaches.
If my son was still pitching, I'd probably still be emphasizing the mental side more for what to work on during a game, as in keeping focus on each pitch as each pitch changes the pitching situation, recognizing what the umpire is giving or not giving and pitching to that if and when it can be taken advantage of. Outside of the mental aspects, since throwing is like hitting in that performance is really about muscle memory, requiring repetition to get consistency, game time just doesn't seem to me like a good time to work on things requiring muscle memory tweaks.
My son and I find game time is useful in finding and prioritizing what needs to be worked on. Not locating that fast ball or change up in a game, then more reps for those pitches than the other pitches before the next game. Next game, still not locating. . . . . MORE reps until you get it right. Not getting that foot down as soon as you should when at the plate in a game. . .then more reps on that. More reps and more reps to get muscle memory so one isn't thinking about it during game time when it's more about reactions as there's very little,if any, time to really think once you're in motion.
Anyway, that's pretty much the what and why of how we've handled game situations during the summer (not much different from regular season except trying to relax much more and add more experimentation and have some fun with it).
