Those of us have needed time off for periods will have taken it as sick leave. Some women won't ever have taken a day sick for periods. Some, like me, will have taken the odd one or two across years, but most months I'm okay with just painkillers. Some women will take one or two days every month, with very severe pains, vomiting, fainting.
It also depends on the job role. I can usually work from home if I need to, and I can make up time when I'm feeling healthier. But if you're meant to be teaching Year 9 at 10:00am, you need to be there in person, or someone else has to cover it.
Where I think the current way of doing things doesn't work well is with employers who use some form of the Bradford factor when looking at employees' sick records. It's possible you get a meeting with HR and they say, okay, we can support you with this, and we'll make this exception for you - and I guess if it is required every month, it might be covered as a disability. But I'd put money on it that some employers will be totally unsupportive and just see it as evidence they shouldn't employ women, regardless of whether someone's work is exemplary the rest of the time - rather than, wow, she has to put up with that, and she can still do her job well.
I do have a problem with us having to behave like periods never happen. Most women of working age will have periods at some point when they're working - not everyone will be able to use the sort of hormonal contraception which stops periods, and for some women, they get constant bleeding, rather than none. Most women will go through menopause years before retirement (especially as the retirement age seems to be getting shifted further and further away.) That can bring all the joys of unexpected timing of bleeding, the likelihood of heavier bleeding and flooding, generally more severe symptoms and less predictability. I don't want special treatment per second, but I do want more flexibility that if I flood, it's okay to go home and get clean clothes and work from home, and I want a stained chair to be sorted out just as a matter of fact, not shame, and it all just to be seen as normal, not a taboo secret. Even jobs which can't be as flexible as others can often have more flexibility than they might currently do, if people are just more imaginative about how we work.
I don't think granting all women period days is necessary - but if women do need to take time off work for it, they should be supported, not penalised.