That article is about broken container filesystems, as in, the root filesystem of the container, but that filesystem is not where you would ever store the data of a database. In kubernetes/eks you would use a PersistentVolumeClaim with an ext4 or xfs filesystem. This would not share any of the overlay filesystem problems and StatefulSets are quite good at managing these.

We run over 900 very stateful MySQL database clusters and several hundred zookeeper clusters in kubernetes on ec2 with ebs successfully. Sure, we've hit our share of problems over the years, but storage itself is solid.