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I know this is not directly relevant, but professional baseball rules list the people who are authorized to be on the field (Players and Coaches in uniform, managers, news photographers authorized by the home team, umpires, officers of the law in uniform (police) and watchmen or other employees of the home club (4.07 (a)).
More directly, NFHS Rule 3-6-6 only permits the "batter, runner(s), on-deck batter, coaches in the coach's box, bat/ball shaggers or one of the nine players on defense... to be outside the designated dugout/bench or designated warm-up areas." This implies that no one else, except media (the rules provide for a designated media area to be set up on the field, with the stipulation that said area is to be considered dead ball territory) , umpires, and possibly active police or security, are to be allowed on the field.
If no one except the aforementioned individuals is to be allowed on the field, then there is no reason for parents to warm up their children during a game, unless a parent is also present at the field in one of the above roles.
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