So you end up with the same number of days off but a bit of flexibility on how to use them.

That's the problem - sick days should not have a "flexibility" aspect to them. You take them when you are sick, so that you can heal and so that you can avoid infecting other people.

Since you don't have a choice about being sick, ideally there shouldn't be a choice about whether or not you take a sick day - but realistically this can't be tightly enforced (at least not with reasonable measures), that it ends up relying on good will, and that there will always be incentives to fake sickness in order to take sick days and incentives to ignore sickness and still go to work (and these incentives don't balance each other out - they incentivize different people differently, widening the gap of unfairness)

But still - even if you accept that real life have such deficiencies - this does not mean one should create policies that make them even more deficient!