What would a bootc system role do?

It would essentially be a wrapper around the bootc CLI. I did not sketch out all details but on a high level I imagine the following:
bootc status: I want the role to report the status of the Image Mode node. That includes information about the current image used on the system and the ones we could rollback or update to. Customers use that for reporting data in UIs or also detect whether a system is impacted by a certain bug (by comparing the digest of the image reported in the status).
bootc upgrade: To look for and fetch an updated image.
bootc switch: To switch the so-called reference of an image. That can come in handy when upgrading to a new major version (e.g., RHEL 10 -> 11). Users can then switch from "myregistry.com/rhel:10" to ".../rhel:11".
bootc rollback: To rollback to the previous image. That's part of the A/B update mechanism.
There is also a bootc-fetch-apply systemd timer/service pair for timed-based updates. I would love the role to also be able to manage that pair. Enable/disable the service. Edit the timer etc.

What is a use case, [...]?

The use cases vary. Some customers use their custom role to manage fleets at the edge. For instance, Guise AI use it in their Edge Ops product where they are currently completing a POC with image mode. Visa are heavy users of Ansible (according to them) and they use their custom role for reporting and to enable manual intervention in case automation fails.
bootc upstream docs - https://containers.github.io/bootc/intro.html