The honest ones take sick days when they are sick. Out of ten sick days they take one or three or eight. The number they take each year depends on how sick they got and how often.
The "work the system" ones take the full allotment every year.
So the system is unfair to people who are honest.
I'm sure there's labour laws that mandate the split. I just can't help but feel that nearly everyone would rather take a guaranteed month of time for "whatever comes up" than "two weeks vacation" and "better make sure you (and your family) aren't sick for more than two weeks annually." Just as I can't help but feel that employers actually prefer the split because dealing with the "'work the system'" ones is cheaper than just treating every employee like an adult by giving them more than a pittance of time away from the office.
You also can't ignore the psychological effect of having to 'give up' time off (for a vacation with your kids, or a visit to your parents on their deathbed) in order to avoid going to work sick. It causes people to go to work sick a lot more often, because they can't anticipate when they will need time off. It also diminishes the rate at which they will use vacation time because they can't accurately estimate how often they'll get sick.
Which leads to "use it or lose it" come December, when your entire company stops working because no one is in the office.
Honestly, I sense people are latching on to my "tough luck" comment without bothering to think the rest of my comment through.
Solve the problem by weeding out the employees who work the system, not by moving to PTO-only and making your entire office sick more often to save a little money.
Without an allotment, employees will generally take a sick day when they're actually sick. Sometimes you'll notice someone who seems to take a lot of sick days. In that case you want to have a friendly chat with them - it's almost never the case that they're just taking free days, rather it's almost always situations like: they're not happy for some reason, they need flex working, they can't afford to repair a car and the commute is worse, they're suffering stress, etc etc. In other words, things it is useful to know about so you can help them (and hence help the company).
Sick day allotments are a way of ineffective managers avoiding confrontations with people: they just end up punishing everyone.
In the US, you have an "allotment" of sick days (say around 10), that defines how many days you can take off sick?
(In the UK) I don't think I've ever heard of such a thing. Surely people are sick however much they are sick? You can't limit your sickness to 10 days a year!
Or, to put it another way: why are you punishing your better employees?