Is it possible to create a k8s Stateful Set without a persistent volume mounted?

I try to create the following stateful set but it fails in 10 seconds while trying to start its only Pod.

apiVersion: apps/v1
kind: StatefulSet
metadata:
  name: dbss
spec:
  selector:
    matchLabels:
      app: db-pod
  replicas: 1
  template:
    metadata:
      labels:
        app: db-pod
    spec:
      containers:
      - name: db-cont
        image: mysql:5
        ports:
        - containerPort: 3306

The error message is not descriptive enough in my opinion:

Events:
  Type     Reason     Age                   From               Message
  ----     ------     ----                  ----               -------
  Normal   Scheduled  5m9s                  default-scheduler  Successfully assigned dbss-0 to minikube
  Normal   Pulled     3m16s (x5 over 5m9s)  kubelet            Container image "mysql:5" already present on machine
  Normal   Created    3m16s (x5 over 5m9s)  kubelet            Created container db-cont
  Normal   Started    3m16s (x5 over 5m9s)  kubelet            Started container db-cont
  Warning  BackOff    2s (x21 over 4m55s)   kubelet            Back-off restarting failed container db-cont in pod dbss-0_k8s-overview(d7c03bf1-051e-47f8-bb72-6b1669584011)

Is it because there is no Persistent Volume mounted to the Stateful Set? Is there a way to see a more descriptive error message to see the actual reason?

I know of the following limitation from https://kubernetes.io/docs/concepts/workloads/controllers/statefulset/#limitations:

Limitations The storage for a given Pod must either be provisioned by a PersistentVolume Provisioner based on the requested storage class, or pre-provisioned by an admin.

Yet I am not sure I understand the quoted limitation correctly. Especially after looking at the events of the failing pods.

It is possible to create a StatefulSet without a persistent Volume

apiVersion: v1
kind: Service
metadata:
 name: nginx-hellow-world
 labels:
   app: nginx-hello-world
spec:
 ports:
 - port: 80
   name: web
 clusterIP: None
 selector:
   app: nginx-hello-world
---
apiVersion: apps/v1
kind: StatefulSet
metadata:
 name: nginx-hello-world
spec:
 selector:
   matchLabels:
     app: nginx-hello-world # has to match .spec.template.metadata.labels
 serviceName: "nginx-hello-world"
 template:
   metadata:
     labels:
       app: nginx-hello-world # has to match .spec.selector.matchLabels
   spec:
     terminationGracePeriodSeconds: 10
     containers:
     - name: nginx-hello-world
       image: dockerbogo/docker-nginx-hello-world
       ports:
       - containerPort: 80
         name: web

in the example on the kubernetes reference page the nginx image they use expects a volume whith the nginx views. That is why in the example they mount a volume.

The terminal responses you provided you're pods are already scheduled but a container in the pod fails to start and kubernetes tries to restart them that is what Back-off restarting failed container means, see this documentation.