You raise some good points, like the kubelet killing off pods in hopes of getting a new pod with juicier secrets associated with it, but nevertheless the ticket mentioned by the sibling comment (https://github.com/kubernetes/kubernetes/issues/40476) sounds like a property that Docker's secret handling already has. It would be great to see Kubernetes work this way, too.
Coincidentally, I'm working on a project that uses Kubernetes and it has a very locked down pod placement policy, so the attack you described would be significantly scoped down. But I don't think the same is true of most Kubernetes deployments.