(Disclosure: I work on Kubernetes/EKS Security at AWS)
I'm curious why they didn't look into using Kubernetes ProjectedVolumeTokens for authenticating to Vault? The tokens Kubernetes issues are not stored in etcd, and they contain pod-specific metadata so they are invalidated as soon as the pod dies (when using TokenReview). Alternatively, they can be used to directly authenticate with Vault since they're OIDC-valid tokens [1].
The semantics around secrets in Kubernetes aren't nearly as robust as Vault, so I was surprised to not see this more clearly called out (ex: list secrets == get all keys and values). Even if you use KMS/AES encryption (which they reference) that doesn't help with access control.