There are major bugs when you move questions to the site (System) or category levels. Backup/restore does not work reliably. For example, MDL-12403.
We have the same problem as you do in your school. We have lots of courses where teachers work as teams (a really good thing!). But when we put all questions in the System level question bank category, backup files/import/sharing cart files ballooned to 500mb or more as the whole Question Bank was sucked into every sharing operation.
Please vote for the above bug which is getting close to five years old--it was supposedly fixed last year but actually it was weakly patched and still it is not fixed for sharing. Also vote for this issue: MDL-41924.
Moodle HQ will listen if enough voices call for changes.