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It's an odd one. I imagine if I was a female who couldn't afford sanitary products, then I would resort to having to ask my parents for them. If they couldn't afford them, then I would assume they were either, very poor or had awful spending habits.
The issue with this scheme, is that the schools get a budget, and they can use that however they see fit. They can spend the whole budget on tampons, or they could spend half of it on pads half of it on tampons or they may not spend the entire budget and may try diddle some money into other aspects of school life.
I think instead of a budget, schools should just get supplies.