There is no reason that I can see why the CONFIG_SYNC_DIRECTORY should need to be writable.
In the case where you want to install and run Drupal on a read-only filesystem, and/or importing configuration from a read-only directory, the current checks prevent installation.
Remove the check that requires $config_directories to be writable in the installer and updater. Also remove this check in the system requirements (the status report).
Review and patch
User interface changes
Two strings (in the installer) are changed. They are shown when the config directory cannot be created
Data model changes