The biggest thing is that Jenkins isn't a CI tool, it's a job execution tool. Whether those jobs are scheduled, manually triggered, triggered by a webhook or otherwise..that's it. It runs the job, records the output and the exit status and makes it easy to read the log of any of those jobs, as well as alternating log rotation of them. It can also manage multiple nodes, distribute those jobs across them or isolate certain jobs to certain nodes.

All that a CI server does is run install dependencies, run the job and then do something with the output. There are tons of plugins for Jenkins to handle those specialized bits of output.

If you want to use Docker images for it, you can do that. If you want to use it to run cron jobs across multiple servers over SSH but centralize the logging and error notification...you can do that. If you want to schedule scaling jobs for expected traffic...you can do that. If you want to trigger Ansible execution...you can do that.

Trigger, Run, Track, Parse. Jenkins does it general purpose, for free, with flexibility to handle many different types of work and different auth tools in one place.

The UI could be better...but it's also hard to tune the UI unless you are specialized for a certain type of work.

The real question is...why bother with a special CI-only tool when you can use Jenkins for that and a whole lot more?