Ok, I understand how sick days work in USA, and while I dislike the idea, I get it from that point of view.
However... carrying over sick days?! That's where it fails to make any sense. Rewarding people who are not sick.. by allowing them to be more sick? Thanks for nothing I guess. Wouldn't it make more sense to give extra sick days to the people who are more sick than others? Accruing sick days will obviously result in people wanting to use their sick days.
So this system really encourages people to advantage of the system, and the whole thing is soo far away from actually wanting to minimize sick days.
The proper way to minimize sick days is to let sick people stay the fuck away. Even if you have to pay them to stay away, that cost will be recouped by all the other people who don't get sick due to some jackass creeping into the office while being sick, because he can't afford to stay at home.
By having a fixed no. of 5 sick days and encouraging people to use 5 sick days, you'll obviously have 5 sick days for every employee. And then some for when they're actually sick.
I am allowed unlimited paid sick days, but yet I have less than 5 sick days annually. Probably closer to zero. Except for covid two years ago which took 3 (working) days and a weekend and was fully reimbursed by the government to my employer anyway.
The way this is done generally is that when someone has been sick for more than a few days, the government will refund up to the unemployment rate to the employer, so they can maintain the employment relationship without having to worry about massive costs. This is a thousand times better for employers and the state and the employees than having to terminate and employ staff constantly due to some artificial "no. of sick days".