Docker is a layer on top of that - it's what prepares the file contents of the jails and looks after them while they're running. I think Docker can even manage FreeBSD jails, although i'm not certain about that.
It's not the production-readiness of Linux containers that is in question here; they're fine, although nowhere near as mature as jails. The doubt is about docker, the layer on top. If you wanted to make a comparison to jails, it would be to whatever the equivalent of Docker is in the jail ecosystem. I'm not sure what that is; either there isn't one, or it's an ad-hoc pile of site-local shell scripts.
I think the point of doing it that way rather than just running Ansible etc on all your containers is that it means you're running N copies of one master image, rather than running N images which you hope are the same because they've been configured the same way. This doesn't seem like a colossal win to me, but some people seem to like it.
Why it's docker that runs Ansible etc, rather than the other way round, i don't know. It's a bit like how rpmbuild runs the build tools that make the contents of RPMs, i suppose. But i really hate rpmbuild so i don't find that analogy very encouraging.
As something of an aside, i get the impression that Docker is most popular with people, or organisations, or people in organisations where for whatever reason developers don't have a lot of control over the configuration of the machines their software run on. That could be traditional inflexible siloed organisations, or small, flexible organisations which just don't have an existing investment in infrastructure automation or the resources to make one. In those situations, Docker gives developers a way to make control the environment around their software without having to configure machines. This strikes me as a workaround to a problem rather than a solution to one, though.
What I see as a problem here for many people is that they don't want to do this all themselves and maybe docker offers conveniences out of the box. I get that. Someone needs to work on the jails tooling to make it more approachable so people aren't inventing the wheel.