When a teacher is absent, the procedure is to get a substitute teacher to instruct the class, so teaching still gets done. Teacher vacation time word still need to be approved or denied. It's not automatic.
When a student is absent, there isn't any way for anyone to learn the information for that student.
Subs are rarely on par with the teacher they replace. Sometimes they are little more than a warm body. An entire class is impacted. If the grade rotates, two to four classes are impacted. So anywhere from 20- to 100+ students can be adversely impacted by an elementary teacher missing a week of school.
When we took my DD out, it impacted no one except her. We took her assignments with us and I taught the material. With a former teacher and attorney to tutor her, she had more than adequate instruction. As a bonus, DH is an engineer. Her education didn't suffer in the slightest. In fact, when she returned, she had passed the rest of her class, as they had gotten bogged down on some material which we breezed through.
Again, know your own situation.
Her teacher did not bat an eye at taking a week off to go on vacation with her fiancé. Other teachers regularly went on vacation too. That is different from when I taught and we could only take one personal day at a time and it could not be on a Friday, Monday, or combined with a holiday. With teachers taking vacation so openly and it sometimes being impossible to find enough subs on Fridays, my attitude changed. We decided vacations were fine for us as well.

). Honestly, the school did not care HOW MUCH someone had paid, but a key point was that this was not just our family vacation for the four of us that we could pay a fee to move to another date. 16 people from 5 different households were involved. I even took in school calendars to show that when we had booked we were working to avoid missing school and that the three cousins were still not missing school, this was planned around a US vacation schedule. Basically, the school wanted a compelling reason why we couldn't just travel during one of the many school breaks and I had to provide that reason and evidence to back it up.