I'm always amazed by how Americans in particular (sorry if you're not, I'm assuming) tend to go from one end of the spectrum to the other without any middle stops in common sense land. I once had a US friend go straight from "we have bad health care" to "we need a violent revolution" with no consideration to... you know, maybe good health care?
I mean, from my perspective it seems pretty obvious that you should only take as many sick days as you need, but you should take all the ones you need, to an unlimited total amount.
Like, that seems so simple. It's how it's always worked in the multiple countries I've lived in. You're sick? You call in sick. You need to be off for multiple days? You ask your doctor to officially declare that you're sick. The company is taking a hit? The government covers your wages during your long term sickness.
This works. We know this works. It's obvious this works.