Your reasoning is... Why shouldn't they? That isn't persuasive. Remember you are talking about taking money from the public.
Maybe someone else should bear the costs. How about the parents perhaps? Shocking concept, I know! But historically the parents have done so. Or the costs could be covered by a grant. Or maybe the tampon companies could simply donate the supplies. Or concerned citizens could organize a non-profits to cover the costs. Or citizens could just donate the funds voluntarily. Or some other way I haven't brought up. No, please don't argue the merits of any of these alternatives since the point is there are other possible funding mechanisms that could be considered. Alternate funding is used for other "needs" at schools, so, to paraphrase you, Why shouldn't this?