I think in this scenario "edge" is a general term for a localised server. I imagine the problem people are trying to solve is just wanting to manage infrastructure in modern GitOps/Infrastructure-as-code ways.
Ultimately people want to deploy all their tech infrastructure in such a way that they can address the "treat X as cattle, not pets" problem. No one wants to be SSH-ing into boxes to update container image SHAs. Kubernetes is one way to do this.
You get a lot of stuff for free with k8s that you'd need to reinvent the wheel for otherwise.
Ultimately people want to deploy all their tech infrastructure in such a way that they can address the "treat X as cattle, not pets" problem. No one wants to be SSH-ing into boxes to update container image SHAs. Kubernetes is one way to do this.
You get a lot of stuff for free with k8s that you'd need to reinvent the wheel for otherwise.