My Quaternion rotation coroutine slows down towards the end?

I have a coroutine that is initiated when the user enters a trigger and then presses a specific key. The rotating as a whole works, but towards the end of the rotation it begins to rotate much, much slower. I have had this issue when using Vector3.Lerp but I fixed that by using speed * Time.deltaTime and another variable to make it smooth. I tried to use a step as per the Quaternion.RotateTowards unity docs but it would just not rotate at all.

void Update()
{
    if (Input.GetKey(KeyCode.Z))    
    {
        Debug.Log("Raycast.");
        if (Physics.Raycast(transform.position, Vector3.down, 1.5f))
        {
            StartCoroutine(Turn(cubeObject));
        }
    }
}
IEnumerator Turn(Transform cubeObject)
{
    Quaternion targetRotation = Quaternion.identity;
    do
    {
        Debug.Log("Begin rotating.");
        Vector3 targetDirection = cubeObject.position - transform.position;
        targetRotation = Quaternion.LookRotation(targetDirection);
        Quaternion nextRotation = Quaternion.RotateTowards(
                transform.rotation, targetRotation, rotationSpeed * Time.deltaTime);
        transform.localEulerAngles = new Vector3(0, nextRotation.eulerAngles.y, 0);
        yield return null;
    } while (Quaternion.Angle(transform.rotation, targetRotation) == 0f);     
}

And if I change the very last value on the last line (Quaternion.Angle) to anything greater than 0, the rotation never ends. I will be locked in rotation until I exit runtime. I'm only trying to rotate fully towards the target just once when the appropriate key is pressed.

As said there is a combination of a couple of issues here

• First you potentially start a lot of concurrent ("simultaneously" happening) Coroutines! You should only start ONE and either make sure you don't start a second one or interrupt an already running one:

   private Coroutine currentRoutine;
   void Update()
   {
       // Use GetkeyDown to check of the first frame the key went down
       // rather than a continuous holding down of the button
       if (Input.GetKeyDown(KeyCode.Z))    
       {
           Debug.Log("Raycast.");
           if (Physics.Raycast(transform.position, Vector3.down, 1.5f))
           {
               if (currentRoutine != null) StopCoroutine(currentRoutine);
               currentRoutine = StartCoroutine(Turn(cubeObject));
           }
       }
   }
   IEnumerator Turn(Transform cubeObject)
   {
       ...
       currentRoutine = null;
   }

• Then you are mixing the global world space direction targetDirection and also world space transform.rotation with a local space transform.localEulerAngles. You want to either do all calculation in local or global space - don't mix!

• Then I think the slowing down can be explained by the fact that your targetDirection might have an offset in the Y axis.

  You do RotateTowards which rotates into the target rotation on all three axes - but then throw away X/Z and only apply the Y component.

  => The closer your rotation comes to the final targetRotation (potentially never fully reaching it btw) the more you see the effect since the Y component of the rotation is already almost "correct" so it now tries to rotate more and more on the X/Z components - the ones you ignore.

  In order t solve this (and in general) I would recommend to stick to Quaternion as much as possible and rather already fix the target direction

   targetDirction.y = 0;
   targetRotation = Quaternion.LookRotation(targetDirection);
   transform.rotation = Quaternion.RotateTowards(transform.rotation, targetRotation, rotationSpeed * Time.deltaTime);
   yield return null;

• And finally never use == for comparing float! You could rather use Quaternion == which uses a reduced precision of 1e-5

   while(transform.rotation != targetRotation);
   // and then make sure to end up with clean values
   transform.rotation = targetRotation;

  or alternatively if you want to stick to the angle an be more precise use Mathf.Approximately

   while(!Mathf.Apprximately(Quaternion.Angle(transform.rotation, targetRotation), 0f));

  which basically equals doing

   while(Quaternion.Angle(transform.rotation, targetRotation) > Mathf.Epsilon);