Keeping them separate as you mention benefits the company for every day of sick time someone can't justify as a day off for something they'd like to do. That

Keeping them separate as you mention benefits the company for every day of sick time someone can't justify as a day off for something they'd like to do. That doesn't make sense to me. It's better and more flexible to have 20 days to use as you want or need. let people roll over some of their unused time and everything is perfect. It seems your way benefits the company and employees who can't manage their time.