The US’s version of sick/vacation days is “you can call in 3 times before a getting fired”

I’ve worked at a lot of places mostly service industry working in kitchens and it seems like most employers will post notice that you can only call in x amount of times before you face termination. Why not just call these sick days? Most countries require a certain amount of sick days where most employers here expect none. Why not just classify these “call-ins” as sick days so we can at least get a few days off if we feel like shit from being overworked