My wife has two very bad and painful days (the first two) every period. I am not sure how she would handle if she had a job.
EDIT: I'm German. Sick leave is completely separate from vacation days here and not limited (although you get less money after six weeks because your health insurance takes over from your employer). Generally I find that one of the only acceptable solution to the problem at hand. Giving half your employees extra days off is a bad idea, conflating vacation and sick leave is a bad idea, and forcing employees to come to work when they're unable to is a bad idea.
the UK has some very forgiving policies on sick leave (https://www.gov.uk/taking-sick-leave). in fact you don't even have to provide a doctors note if you take just a couple of days off.