Google Classroom is the worst LMS I've ever used and the "log in from any machine and have your files" thing was solved by Active Directory decades ago...
The reasons schools ate them up os because they're cheap and were the most readily available laptops during a shortage. I really doubt much else was on anyone's mind.
I also have a few qualms with it:
1. For a Linux user, you can already build such a system yourself quite trivially by getting an FTP account, mounting it locally with curlftpfs, and then using SVN or CVS on the mounted filesystem. From Windows or Mac, this FTP account could be accessed through built-in software.
2. It doesn't actually replace a USB drive. Most people I know e-mail files to themselves or host them somewhere online to be able to perform presentations, but they still carry a USB drive in case there are connectivity problems. This does not solve the connectivity issue.