My opinion is that as long as the stats are scored objectively the coach shouldn't care that the stats are made public. I'd be suspicious of a coach that tries to keep the stats secret. If he's making coaching decisions objectively and fairly based on performance as he should be then the stats should be his ally and not a threat. I think coaches that try to keep the stats secret do so because they don't want to be accountable for the decisions they make and are typically not setting their lineups and defense based on performance but on some dubious criteria (favoritism, opinion not based on fact etc).
Let me also say that as long as the games are played in public there's really no way to keep the stats secret (unless of course you blindfold all the spectators) because every spectator could keep their own stats if they really want to know what they are.
One last point. I'd encourage coaches to use the stats as a measure and incentive for good performance. For instance, at the beginning of the season spell it out to the players and parents how you will set your batting order and let them earn their spots. For example, the 1st batter will be the batter with highest OBP. Batter 2 will be the 2nd highest OBP, 3rd batter highest combined OBP + SLG, 4th batter highest SLG then 5-9 in descending order of AVG or OBP. That way, if a kid performs, they are rewarded and it's clear to everyone. I also suspect most coaches would win more games this way because they wouldn't be captive to their own opinions.
Nothing is more disheartening or frustrating to a child than not understanding why they aren't rewarded for good performance and at the end of the day it's about the kids, not the coaches or the parents.