I currently accrue an "all-purpose" leave. 4 weeks a year, covers everything generally. The 10 federal holidays are separate of course. Bereavement and disability being special cases. Time off without pay would be fine if approved for some special circumstance.
If I choose to leave, the all-purpose leave gets paid out just as unused vacation time normally would. If I get laid off, the same deal applies. It carries over from year to year (with caps of course, generous though). Theoretically you could have up to 8 weeks built up, resign in December, and get the full 8 weeks paid out in pseudo bonus. All in all, it makes for a nice safety net should one of those two occur. Mandating "sick leave" would likely mean that my 4 weeks a year would surely become something like 2.5 weeks per year, which then cuts in to how much I could accrue and then get in pay out should choose to bank it.
And yes, if you're going to give me X number of days that MUST be used for "sick leave" purposes only... where I get no potential benefit for not using it... well, I'm going to be sick pretty much for X days per year.
Worked for a big local engineering company years ago that went from a "2 weeks sick / personal time" policy to "Unlimited sick / personal time". Then they started needling people once they went over 1 week of "unlimited personal time" in a 12 month period.