You’re right, of course. That’s what I get for answering while undercaffienated. I mixed up “you can update the app while running, from within the app” with “the app will update itself periodically”.
For what it’s worth, the Plex container can be updated from the command line:
[root@rockbox ~]# docker exec -ti plex-linuxserver.io /etc/cont-init.d/50-plex-update
Atempting to upgrade to: 22.214.171.12401-53fa66811
2017-11-02 07:52:50 URL:https://downloads.plex.tv/plex-media-server/126.96.36.19901-53fa66811/plexmediaserver_188.8.131.5201-53fa66811_amd64.deb [107908936/107908936] -> "/tmp/plexmediaserver_184.108.40.20601-53fa66811_amd64.deb" 
(Reading database ... 11383 files and directories currently installed.)
Preparing to unpack .../plexmediaserver_220.127.116.1101-53fa66811_amd64.deb ...
Unpacking plexmediaserver (18.104.22.16801-53fa66811) over (22.214.171.12485-ef7796e43) ...
Setting up plexmediaserver (126.96.36.19901-53fa66811) ...
There might be a smaller window of service disruption when updating this way instead of just restarting the container, but yeah, it’s not going to be huge, and it’ll be easier to just restart a few containers than to figure out for each one how to auto-update them.
To get back to the original issue: it’d be nice if there was a way of doing a bit more with cron from the web UI. Maybe not a full blown crontab editor (although that would work for the power-users), but a slightly more extensible system of adding and managing tasks.