What about persistent storage and access costs ?
And couldn't that then over time increase managed k8s costs significantly ?
If you have a data intensive service, it surely would add up, but it's not specific to Kubernetes. If you go with VMs or a Serverless deployment, you'll have to pay it too.
If you're speaking about the storage and data transfers related to the Kubernetes control plane itself, I don't believe it represents a significant cost, even with a large cluster.