I agree that there is a big grey area on what is too sick to work, but with my proposal at least we are a big step further and instead of the employer deciding for you (who wants you to work for them) or you deciding on your own (who might not want to come to work after a night partying), there is now an (hopefully) independant entity, the doctor who decides.
But I have to admit that of course the doctor can only listen to the patient and decide based on that, because there is just no way to measure pain/sickness objectively. So in the end we have to trust people to decide on their own if they are sick.
With your proposed solution of x sick days, I guess that many people that are actually too sick for work have to work just because they don't have enough days, while some that don't get sick might use their sick days anyway, because they have them. And even with my solution, realistically there will be a lot of people going to work when they should rest, while there will also be people that use the system to rest after celebrating.
I don't think a perfectly fair system is possible, but I prefer the system where people are not exploited and supressed.
Coming back to your argument on periods, like I said, there is no way to measure someones pain besides asking them, and ignoring their answer is not the solution, so yes women should be able to take leaves for period pain.
And yes, men should be able to take leaves if they feel like crap, even if that might mean taking of a day off that they might have been able to work. In the end the grey area is not perfectly convertable to able to work/not able to work.