The 4-girl rule in the summer is an exception that allows high school coaches to bypass the 10-day rule and coach up to 4 of their players on a travel team all summer. It's an odd exception, but you take whatever crumbs the OHSAA throws your way.
I believe the purpose of the 10-day rule is two-fold. One, as others have stated, is to keep high school coaches from forcing girls to practice or play all summer with the high school coach. But I think the main reason for the rule is that the OHSAA thought that with the rule in place, girls would have the summer off from softball (or whatever sport), except for 10 days.
The OHSAA and similar organizations abhor club sports (just watch the video they make high school coaches view) and my guess is that when these rules were passed, they had their heads stuck so far in the sand that they didn't dream families would actually WANT to play ball in the summer and that the rule would help club teams prosper. I believe that the bureaucrats in the OHSAA thought that because they hate the idea of athletes playing a sport outside of the high school season, therefore everyone must hate the idea and they would be the ones to save families from such an atrocity. Yes, that is a cynical view, but I'm just going off of the comments that I always hear and read from school administrators, which make up the OHSAA.
What they don't realize is that they ultimately have no control over what families do in the summer, thank heavens, as they have no business even trying. I don't think it's the summer rules that hold back development of athletes, it's more the total restriction on coaching in the school year outside of the season. The rules are so geared toward two-and three-sport athletes that the one-sport athlete is unfairly kept from receiving coaching for most of the year. It would seem to me that some allowance of time for coaching would make sense, if not just getting rid of the rule altogether. Yes, some minority of coaches will insist that athletes play only their sport. But if coaches push too hard about playing only one sport, they will eventually lose players.