I agree that is what sick leave is for. If you have agonising period pain, you have a condition that prevents you from working that day, and that's okay.
We can't claim that women are every bit as effective and reliable at work as men, if we're offered time off for periods (whether we suffer badly with them or not) and are offered flexi time time when men are not.
Then when periods are over we ask for menopause accommodation as well.
We really can't have it both ways. We will simply make ourselves unemployable.