The reason, I believe, is that there are random checks by the health service to ensure people on sick leave are actually sick. But if you only take a day off due to a headache, by the time it gets registered and checked you could have already got better - so your claim is hard to verify.*

A dishonest employer could easily defraud the system by claiming a lot of individual, unverifiable "sick days" and getting the state to pay for a nice chunk of his payroll expenses.

By contrast, an employer gets alerted sooner of an absence and is in a much better position to guess whether an employee claiming fake sicknesses. In case of suspicion they're legally allowed (at a small fee) to have a physician check on their employee from day 1.

* now that I think about it, with everybody having a camera phone nowadays, this might eventually be solved - a video call might not be enough for a diagnosis, but it can probably tell "yep you're sick" with a reasonable degree of confidence?