> From the sysadmin viewpoint, /var is managed through "retention" (scheduled rotation, scheduled flushing, logrotate, crons, etc), and "backups" where needed.
Right. And 'Docker for /var' would be something that made all that easier. It would make it really easy to set up live, secure, restorable, backups of essential data; to rotate, compress, and delete logs; to extract all important logs to a separate host, and aggregate and index them, etc. At the moment, a configuration management tool can help you set this up, but you still have to write the configuration management script by hand.
Configuration Management may help to set non default permissions under /var/ paths, or to check for default permissions status, or prepare business logic automated actions over that variable data.