I'm pretty sure the people ITT are going to disagree with me, but vacation is a luxury, sick days are a necessity. If I missed weeks of work I wouldn't also take a vacation that year regardless.
In many places (Europe, generally?), vacation days are earned. At least in the Netherlands if you were absent for weeks due to illness (for which there is no fixed pool of days), and decided not to take any vacation days, you'd either have some of your vacation days rolled over to the next year or they'd be paid out to you with salary and taxed.
It's not a luxury in the slightest. You'd have earned them just as you earned your wages.
But parental leave is considered as work, so if you come back after your parental leave, you have your full amount.
There's no distinction, at least not with the statutory holidays. You earn them as you earn your wages and there is no adjustment for illness.
Why wouldn't you?
If you missed weeks of work from an illness, those weeks aren't time where you could see family, see the world, relax, and be human. They don't satisfy the same long-term needs as fully-disconnected vacation time satisfies.