When I went to school, no “refreshments” of any kind were allowed in the classrooms. If you were thirsty, you could get a drink at the water fountain between classes. Seems like this rule was not outrageously cruel at the time.
When we were in school we didn’t have 10 min walks to get to the next class and only 5 min to get there
We didn’t have schools with 1000 kids per grade
It's hard to imagine what the environment is like in many schools. FWIW, the best solution is a water bottle even if it's a disposable one with the child's name on it. An even better solution in many cases is online home study public schools.