Good points for sure.
In my experience, kids who "take the summer off to workout and build velocity" don't actually push themselves hard enough to make velocity gains a reality. And then because they're not pitching competitively also, it ends up being the beginning of the end. Seriously. I can't tell you how many kids are right on the cusp of a break through, and then make the decision to "take the summer off" from games, and it just doesn't work out. Now, if you were instead training at IPI in Fla, or at Cressey Performance in MA, or something like that type of structured environment every day -- then maybe. But that's super expensive and generally not what we're taking about here with most kids.
Look, I totally GET the fact that there's A LOT of "doing nothing" in baseball. Especially for pitchers. But that's the game. That's why kids play lacrosse. Continuing to improve during the season requires a certain type of kid who will eek out what little time there is to make improvements, throw a pen, do pfp's, do rotator cuff exercises, run poles, do med ball stuff or plyos in the outfield, etc.