I really agree with the concept that period issues needing flexibility at work shouldn't be taken as sick leave but that there should be ways of working around it, in the same way I've seen done for pregnancy (ie someone with hyperemesis being temporarily moved from working in a ridiculously busy a&e to a ward where they have regular rest and meal breaks and easier access to a toilet)
a friend of mine has severe depression and his job, when he is well enough to work, is very flexible just by its nature. On good days he will work a 12 to 14 hour day despite officially working 9-5, this means on the days he just can't face the world he can stay in bed til life feels a bit better.
I like the idea of 'health' days as well as sick days. You're not unwell as such but something - your horrific period, your shitty low mood, your insomnia that has meant you only slept 40 minutes and don't even feel safe to drive to work - means you need today off work. No 'back to work' meetings, no having to explain on the phone why you just can't work today. Just a certain amount of days a year where you can phone in and say 'I can't come in today as its better for my health I stay at home'