Generated meshes/materials cannot be made into prefabs?

I'm not sure if I'm doing something wrong, if this is a bug, or if it's intended behaviour. But if you have a component that generates a Mesh or a Material (perhaps others too), it seems that you cannot make it into a prefab and have the generated objects stored with it. This seems strange, because you can save/load scenes with generated meshes just fine, so it's not as if it's something that cannot be serialized.

Here's an example component that demonstrates this issue:

 using UnityEngine;
 
 [ExecuteInEditMode]
 public class GenerateMesh : MonoBehaviour
 {
  public Mesh myMesh;
  
  public void Awake()
  {
  if (myMesh == null)
  {
  myMesh = new Mesh();
  myMesh.name = "My Mesh";
  myMesh.vertices = new Vector3[] {Vector3.up, Vector3.right, Vector3.left};
  myMesh.RecalculateBounds();
  myMesh.RecalculateNormals();
  
  var meshFilter = gameObject.AddComponent<MeshFilter>();
  
  meshFilter.sharedMesh = myMesh;
  }
  }
  
  public void OnDestroy()
  {
  Destroy(myMesh);
  }
 }

Simply attach this component to a GameObject and observe that it creates a mesh and assigns it to both the MeshFilter and the public myMesh field. If you then drag the GameObject into the Project window to create a prefab, it will lose the Mesh and say there's none.

I'm aware that you could create a Mesh or Material asset to get around this, but in my actual code, I generate my Mesh + Material in Update() whenever it detects the public fields have been modified, so it would be very impractical to create assets potentially every frame.