That said, Google, to my understanding, does run a completely containerized infrastructure internally, including databases and other stateful things, so it is not wildly off to suggest running a database on Kubernetes.

Kubernetes might be simpler than Borg in so many ways (let me count the ones I care about...), but it also has better features that Borg did not implement (labels and selectors) or that are offered only by some other internal services, which obviously are configured through very different mechanisms (ingress).

Wow, I'd never heard of Fargate until this. It seems so somewhat obvious now for things that Lambda doesn't fit. Heroku for containers, not VMs.