Pitchers need at least 4 weeks off from all throwing , whether its after the regular summer season, or after fall ball. My DD's college coach shut her down for 4 weeks after the summer games last season , and she is now shut down from all throwing, pitching until she goes on campus in a couple weeks.
They need time to rest!! Once they get in high school they will be going from end of February through mid May, even into June if they play deep into districts, regionals, states. Its not uncommon for them to start travel as soon as they are done with HS ball. Thats 6 months of ball! If you throw another month or so through the fall your approaching 8 months.
Pitchers will get burnt out! they will get tired, develop bad habits associated with burnout or just being tired, and risk possible injury to their arms,shoulders, elbows ,legs, feet. The arms/shoulders are not the only part of a pitchers body to be worried about. DD has developed foot problems, toe problems, from the constant impact of stride after stride during the season. Knee problems are not uncommon either. You must find time to shut them down to rest.