If you have any long-running operation that could be interrupted mid-run by any network fluke (or the termination of the VM running your program, or your program being OOMed, or some issue with some third party service that your app talks to, etc), and you don’t want to restart the whole thing from scratch, you could benefit from these systems. The alternative is having engineers manually try to repair the state and restart execution in just the right place and that scales very badly.
I have an application that needs to stand up a bunch of cloud infrastructure (a “workspace” in which users can do research) on the press of a button, and I want to make sure that the right infrastructure exists even if some deployment attempt is interrupted or if the upstream definition of a workspace changes. Every month there are dozens of network flukes or 5XX errors from remote endpoints that would otherwise leave these workspaces in a broken state and in need of manual repair. Instead, the system heals itself whenever the fault clears and I basically never have to look at the system (I periodically check the error logs, however, to confirm that the system is actually recovering from faults—I worry that the system has caught fire and there’s actually some bug in the alerting system that is keeping things quiet).