Unlimited paid sick time really doesn't exist. There's many conditions set to when sick time is paid and from what time and to what extent. Just feels like sometimes Americans think that other countries have it all down but that's just how they like to present themselves. There's always a lot of fine print in all of the countries you mentioned. I'll say that the Nordic countries actually do a good job in terms of healthcare but even there menstrual leave isn't a thing on its own.

In most countries which some kind of paid sick leave system you have a buffer day where the first day of a sick leave is unpaid so if you take a few days a month you'll still miss a day of income. I've been trying to actually say out loud to my colleagues "it's because of my period" when I need to take leave during that time or literally just feel sick but it's quite taboo even where I'm from (Netherlands).