Enemy follow Camera

I've got the following script attached to the enemy to make it move towards the camera:

 using UnityEngine;
 using System.Collections;
 
 public class EnemyMovement : MonoBehaviour
 {
     Transform player;
      NavMeshAgent nav;
     
     void Awake ()
     {
         player = GameObject.FindGameObjectWithTag ("MainCamera").transform;
         nav = GetComponent <NavMeshAgent> ();
     }
     void Update ()
     {
         nav.SetDestination (player.position);
     }
 }
 
 

The problem I have is that it only follows the camera if it get close to the enemy on a flat plain; it won't follow the camera into 3D space. The scene has a navmesh (and the enemy a navmesh agent) which I guess is causing the problem. But I also tried duplicating the model, removing the navmesh agent and using this script:

 using UnityEngine;
 using System.Collections;
 
 public class EnemyMovement : MonoBehaviour
 {
     Transform player;
     public float speed = 6f;
     GameObject enemy;
 
     void Awake ()
     {
         player = GameObject.FindGameObjectWithTag ("MainCamera").transform;
     enemy = GameObject.Find("Enemy");
     }
     void Update ()
     {   
         enemy.transform.LookAt(player.position);
         enemy.transform.position += transform.forward * speed * Time.deltaTime;
     }
 }
  

But this did nothing. How can a make the enemy move towards the camera, wherever it goes?