US Academia and sick days In a comment to their answer to the question Faculty member brought sick (feverish) child to class - is this unethical?, the user Anonymous Physicist writes:

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@quarague It's okay to cancel class for a sick child in US academia, but some US workplaces do not grant sick days for sick children. US academics don't have sick days at all.
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I come from a European country where the concept of "Sick Days" is different than in the US (indeed, I understand the word "sick day" only because of Workplace SE and I am still not sure I understand it correctly) -- as I understand, a sick day is day you can take when you are sick and still get paid.
My question: Is the comment true, i.e. do US academics not get sick days? Is it really true universally in the US (i.e there is some "law" or regulations that universities are not allowed to give sick days to their employees)?
Is there some other system in place or do US professors really just not get paid when they are sick? (If not, why hasn't there been some strikes/demands/movements? Surely tenured profs don't need to worry to get fired when they make demands?)

Please note that while those questions may sound silly for a US person, US and European employment laws differ a lot and the whole concept of "sick days" is really complicated to me.
For full-time faculty, the question doesn't really apply well because faculty aren't paid hourly or daily.  In the departments I've been involved with, the policy is that faculty handle their own classes and minor illnesses.  That is, if I need to cancel class one day then what that means for the class is up to me.  Maybe I have a TA teach it, or I offer a recorded lecture to fill in time, or even just cancel the class and adjust material accordingly.

What it comes down to is whether I can meet the obligations for the class while handling my illness.  For major illnesses where that isn't true, the department would schedule someone else to teach and I would look at my short-term disability benefits, which are commonly available in large US universities.  The unfortunate exception is an adjunct faculty member, who simply teaches contract-to-contract, and may not even have benefits through the university.