We rarely do the AI on cruise ship days.    However, Cozumel shoreline is predominantly ironshore so the limited sandy section is where the large tourist beach clubs and many of the hotels offering AI day passes are located and whilst PAYG may be available at non-peak times, it is not guaranteed.    The other option for sandy beaches is east side but not recommended during sargassum season or for swimming. Also what you save on non-AI  you will pay in transport so no cost savings.