Indeed and if you bring up a Kubernetes cluster today on AWS using their EKS there is no overlay network. There's a CNI but no overlay.
https://github.com/aws/amazon-vpc-cni-k8s/blob/master/docs/c...
In the end there is no ideal scenario; boils down to what works best for the use case (or what is the 'least worst' solution). Sometimes it gets you down, but those imperfections can turn a churn job into an interesting one.