For instance, you could run your package manager across all containers to see if they have packages with known CVEs. Or manage the filesystems of all containers on the system (the usefulness of this is only clear with filesystems like ZFS and btrfs). This is effectively what you can do with Solaris Zones.
These kinds of improvements to usability aren't as sexy now that everyone is really excited about Kubernetes (where you blow away containers at whim) but it is useful for the more traditional container usecases that Zones and Jails. LXC (and LXD) is probably the one Linux container runtime that is closest to that original container model.
There's also a very big security argument -- it is (speaking as a maintainer of runc) very hard to construct a secure container on Linux. There are dozens of different facilities you need to individually configure in the right order, with hundreds of individual knobs that some users might want to disable or quirks you need to work around. It's basically impossible to implement a sane and secure container runtime without having read and understood the kernel code which implements the interfaces you're using. If containers were an in-kernel primitive then all of the security design would rest in one single codebase, and all of the policies would be defined by one entity (the kernel).
You can also do this on Linux with NixOS, where you can define the system and all containers it runs declaratively. Updating the system will update everything, including the containers (of course, you can also pin the containers or packages in the containers to specific versions).