I am not familiar with how onsen works, but the water is being refilled over time right? So if they didn’t add back the food, won’t the water become too much water later on? Like when we reuse a tea bag
I know they take a shower before they get into the bath but that doesnt stop the crotch or junk from having indirect contact with the foods. Even the pits... if it was a personal bath sure not go for public/shared though