A much better solution is vacation days and unlimited sick days, as well as generous work-from-home opportunities for days when you're under the weather but not too sick to work.
People who do not make such choices rarely get sick for more than the odd few of days a year. Why should they subsidize poor choices? Not being sick a lot is a reasonable and sensible professional expectation.
The alternative to to accrue leave.
Where I work, we have vacation/sick/personal leave. There are different rules for each, and vacation time accrues and you get paid upon separation.
2. It gives people an incentive to come into the office sick. The result is that half the office is ill (but showing up!) all winter. It's pretty disgusting.
If you're trying to build a polar vortex of disease, then implement a pooled PTO system. If you're trying to build a company, then don't. It's that simple. What are you trying to build?
Here's how I would set it up:
* Three weeks minimum vacation. (Investment banks have mandatory vacation and it's not a bad policy.) In tech, that wouldn't be a hard-and-set rule, but taking little vacation should be the choice that needs to be justified. Five weeks paid, anything beyond that is unpaid leave which can be taken without stigma.
* Don't come in if you're sick. It happens to all of us. If you're going to lose more than 10 days per year to health issues, talk to HR about accommodation and we'll try to make something work. If it's less than 10 days (e.g. colds and flus and stomach bugs) then just stay home.
* Don't worry about emergent personal issues. Let people know where you're going, then go. Come to work when you're ready to concentrate on work, not when you have nonsense hanging over your head.