Most women I know would be empathetic but ultimately find this insulting, that the world thinks they can't act normally during their periods. I'm not going to pretend to know what it's like, but I know women mostly do work through them.
Also, women almost all react differently, and some have had treatments to block them indefinitely. But an employer would never know any of that, and human nature says a bunch would demand a week off whether they needed it or not.
There's no way to verify, like some places verify medical absences with a doctor's note.
Better to just use sick days if it gets overwhelming.