Why is my animation jumping to the last keyframe when set in script?

I am trying to rotate a gameObject by scripting it. This gameObject is a bone added in SkinningEditor, which should not make a difference. The script I wrote below is attached to the bone.

Code (CSharp):

1. using System.Collections;
2. using System.Collections.Generic;
3. using UnityEngine;
4. public class DeformBone : MonoBehaviour
5. {
6.      void LateUpdate()
7.      {
8.          setAllCurves();
9.      }
10.      private void setAllCurves()
11.      {
12.          var angle = Quaternion.Euler(0, 0, 5);
13.          var rotXcurve = AnimationCurve.EaseInOut(0, 0, 5, angle.x);
14.          var rotYcurve = AnimationCurve.EaseInOut(0, 0, 5, angle.y);
15.          var rotZcurve = AnimationCurve.EaseInOut(0, 0, 5, angle.z);
16.          var rotWcurve = AnimationCurve.EaseInOut(0, 0, 5, angle.w);
17.          // set the curve here
18.          AnimationClip clip = new AnimationClip();
19.          clip.legacy = true;
20.          clip.SetCurve("", typeof(Transform), "localRotation.x", rotXcurve);
21.          clip.SetCurve("", typeof(Transform), "localRotation.y", rotYcurve);
22.          clip.SetCurve("", typeof(Transform), "localRotation.z", rotZcurve);
23.          clip.SetCurve("", typeof(Transform), "localRotation.w", rotWcurve);
24.          // play the curve here
25.          if (gameObject.GetComponent<Animation>() == null)
26.          {
27.              // add the component
28.              var animation = gameObject.AddComponent<Animation>();
29.              animation.playAutomatically = false;
30.              animation.wrapMode = WrapMode.PingPong;
31.            
32.          }
33.          GetComponent<Animation>().AddClip(clip, "rotateyo");
34.          GetComponent<Animation>().Play("rotateyo");
35.      }
36. }

However, the animation jitters quickly back and forth, jumping from keyframe to keyframe and then it gets faster and faster until it just looks a bit crazy. I want it to rotate at the angle indicated slowly. I have tried putting this in Start() - this only jumps it to the last keyframe where it stays, and FixedUpdate/Update where the same thing happens.

I can see in the Inspector that I have successfully added an Animation to the bone and that the curves are being set up properly. What am I doing wrong?