I work in K12 education trying to help teachers integrate technology. The answer to your question is more complicated than you think. Google Apps make sense for us because we have a ton of users (students) who move between different devices throughout the course of a day. With Google Drive, Sites, calendar and mail, their stuff follows them around.
Best yet, it's free. And it's actually more free than LibreOffice. There's nothing to download and nearly nothing to maintain. We have to make sure our devices have Chrome installed and we have one guy who manages the domain and keeps the database of users and passwords working for 56 schools and associated administrators, teachers and employees. As long as our network stays up, we don't have a problem, and most school systems these days have a pretty robust network connection and infrastructure, so long as they are spending their federal e-rate money wisely.
On the privacy side, Google has language in their Apps domain contracts that protects student data. Is is perfect? Probably not, but it falls in the "good enough" category.
We are still transition to Google. There are lots of teachers and students who use MS Office more than Google, but it's a process. If I had my way, we would continue the transition and then ditch MS Office completely in a few years, replacing it with Libre as a backup for those times when you have to have a workstation-based office suite. This has the potential to save a massive amount of money and yet still be MORE effective than what we were doing.