The problem is that people will have a huge party weekend then be hungover on Monday, or want to spend Friday getting the party started. And they decide this at the last minute, so they take a sickie instead of planning in advance. Often you cannot take AL ~1-2 weeks, you need to plan it out in advance.
Why? Do they at least allow unpaid negative sick leave? Some surgeries and heart operations and things need a month to recover.
Pooling it IMO isn't always the best result. The problem is that the people who get sick a lot are the ones who also get a lot of work stress, the work stress compounds into more sickness due to lost sleep / lost vitamin D / etc., and they are actually the ones who need the holiday time the most. People who have zero health issues probably have good work life balance already, at least enough to get exercise, eat healthy, and sleep well, and although they too deserve holiday, they need it less than the people who are already exhibiting the symptoms of overworking (lots of body issues).
Especially in the US where many only have 2 weeks of paid leave, or in many cases, 0 weeks.
Most jobs have at least: 4 weeks paid leave (annual) 2 weeks sick leave (which may require a note depending on company policy) 12 months parental leave for new/adoptive parents 6 weeks of Long service leave after 7 years, growing at the rate of roughly one week per year thereafter In addition to this we have 13 days of public holiday
Source: Australian employment lawyer
Why not just give them enough PTO so they can get a few long weekends here and there, and they won't need to lie.