Kubernetes is designed specifically to abstract the clustered nature of multiple machines into something that's singly addressable. The upcoming addition of federation is intended to add another abstraction on top of that, allowing the addressing of multiple clusters as a single cluster.

The primitives currently included in Kubernetes are mostly geared towards scheduling containerized services onto multiple machines in order to achieve a desired state, but it's only that containerization that has the stateless/ephemeral connotation. Kubernetes is perfectly capable of handling stateful storage and it's as simple as mounting a storage volume: https://kubernetes.io/docs/concepts/storage/persistent-volum...