Schools and Free Software
Most schools use propietary software for everything, there are some exeptions but those are usually accidental. I don't know about the situation in other countries so I will write about what I see in Estonia.
Schools use Windows, Google Services (Classroom, Slides, Docs, etc.), Zoom and much more propietary software. This is especially important now that there is more and more school work online. It is sadly necessary to use those services for school because if you aren't on Google Classroom for example you will not have acces to homework and other things. By forcing students to use propietary software at school they are locking the students into a propietary software ecosystem. Even if a student wanted to stop using propietary software they couldn't.
Why is using propietary software so bad? Because the user doesn't have control over the software, instead the software is controlling and tracking the user. This is not the case with free and open source software (FOSS) because FOSS is made in a way that respects the user: the software doesn't track or control the user, the software can be forked and changed when necessary.
Why do schools prefer propietary software? I assume that it's because they don't know about the flaws of propietary software and for them it's easier to use it because they are probably more familiar with it. Using free/libre software in schools requires some effort from the school so it is very easy for them to go the easy route and use Google, Windows, Zoom. Windows comes preinstalled, setting up Google Services for school is simple, using FOSS alternatives often requires you to host them on a server (Not strictly necessary as it is possible to use public instances).
Cost? A lot of propietary software has some kind of a cost - usually a subscription or a license. Free (as in freedom) software is usually also free as in gratis but hosting the software on a server would require the school to pay for a VPS or for electricity and internet if hosting it on their own server. VPSs aren't usually very expensive so I don't think it would be a lot more expensive for schools to use free software. With the servers there would also come some other expenses. Overall the cost would probably be similiar.
Should a school prefer convenience over the freedom and privacy of it's students?
I have put together a list of free and open source alternatives for software commonly used in schools: List