Make an enemy only rotate with navmesh agent

I did it in one of my games by turning off updatePosition while it rotated to the next waypoint, and then re-enabling updatePosition once the agent had rotated to face the new target.

Here is a working example, could probably be optimised a bit. Put this script on an object with a NavMeshAgent, and populate the targets[] array with your waypoints.

 using UnityEngine;
 using System.Collections;
 
 public class NavMeshFollower : MonoBehaviour {
     [SerializeField] Transform[] targets;
     int index = 0;
     NavMeshAgent agent;
     // Use this for initialization
     void Start () {
         agent = GetComponent<NavMeshAgent>();
         agent.SetDestination(targets[index].position);
     }
     
     // Update is called once per frame
     void Update () {
         if(agent.hasPath && agent.remainingDistance<0.5f) // Reached target?
         {
             agent.updatePosition = false;
             StartCoroutine(GetNextTarget());
         }
     }
 
     IEnumerator GetNextTarget()
     {
         index = (int)Mathf.Repeat(++index,targets.Length); // Get next target point from array
         var targetPos = targets[index].position; //Cache new target point
         var agentPos = agent.transform.position; // Cache agent position
         agent.SetDestination(targets[index].position); // Tell the agent where to look
 
         var VecToTarget = targetPos - agentPos; // Calculate a vector from current agent position to new target
         //Debug.DrawRay(agentPos,VecToTarget,Color.red,2f);
 
         while(Vector3.Dot(VecToTarget.normalized,agent.transform.forward.normalized)<0.99f) // Check if agent is pointing to new target, and wait while it isn't
         {
             yield return null;
         }
 
         agent.Warp(agentPos); // Reset agent position
         agent.SetDestination(targetPos); // Reset agent target
         agent.updatePosition = true; // Off we go!
     }
 }