It would be useful if you could compile a list of commonly requested directories, because from my experience /home or /media is usually enough for most use cases and so if there are common use cases for other directories we would like to understand them so that eventually we could attempt to craft strict interfaces allowing such accesses.
Additionally, there is an open PR (see interfaces: add system-backup interface by jdstrand · Pull Request #6436 · canonical/snapd · GitHub) which hopefully will eventually add a system-backup interface which would allow read-only access to any directory on the system (other than /dev, /sys, and /proc) which sounds like it would partially solve your use case.
Not sure what to do about the network mounts access, sounds like it could be a GUI bug with the file chooser not searching all paths properly or it could be something else entirely.