One of my old bosses basically asked you what hours you wanted to work, there was a mixture of f/t and p/t.
I was young and single so worked long days Mon - Thu and had Friday afternoon off.
1 person chose term time working, another mornings only etc.
if we have upset students in distress, for example, someone needs to be there to deal with them, which means not everyone can have these flexible hours.
Rubbish, you make sure you have enough people in the office at all times, I worked in a hospital that did this (we had on call for emergencies), if patients were booked in we had enough staff in, if no one was booked in we had a min of 1 cath lab 'team' so one tech, 2 nurses, 1 radiographer.
OP have you considered 'on call' - ideal for people with older kids, you can take the time off in the school holidays but know you have to come in when needed, you are paid a small amount for being on call and wages when called in. I'm thinking a parent of early teens, where they are quite independent but you might not want to leave them all day.
OP
Think about not just parents but other people who might benefit, some people may want a day or half day for religious reasons, or because they shop for an elderly neighbor etc etc.