My response was as much of a generalization as yours was. Before I explain how I operated as a coach let's be perfectly clear your son would play for the team on my terms and you would not interfere. You would not play agent. Players play, coaches coach and parents support the team. Part of my responsibility as a coach was to teach parents how to become parents of athletes. Now that we have the rules clear I'll explain how your son would come to be on my team starting at 13U. At 11U and 12U the travel team only played in a Sunday doubleheader league with our LL's prospective all-stars. LL didn't play on Sunday.
At some point in the summer there would be a casual comment from one of the coaches to you asking if your son would be interested in playing for our team the following year. If so, call at the end of the summer. We never stoled players from teams. We didn't chase players. We made one comment. The rest was up to the parent. The other way was you would have seen how the team was run, how fair things were done, how pitchers were not overused, and except for the one whiny dad who didn't understand why his son wasn't an infielder, parents would have said good things about the team.
When we talked I would have explained how positions are earned, how much playing time every player would get at a minimum, how pitchers would be handled, the backgrounds of the coaching staff, what instruction would be the focus and the player and parental behavior expectations. I would answer your questions and you would make a decision. At that point if you paid attention you wouldn't have felt the need to present your condesending quiz worthy of a ignorant rec ball coach.
If you started telling me how your son would be used, or presented me with your little quiz, I'd tell you I'll get back to you in the future. you would probably be able to read the declining interest in my body language. One year I turned away two studs due to their parents. I figured let the parents try to run another coach's team.
The way we operated worked. None of the pitchers ever got hurt. We turned away players every year. Most parents like a coach who doesn't play his son at short because he has a better one. We weren't trying to win state championships. We were trying to develop high school players. We still finished as one of the top ranked teams every year. Eleven of fourteen of the 13U players are starting soph year of high school. One quit baseball to focus on another sport. Two are in powerhouse programs where they will start as juniors.