Material.SetTexture cannot operate faster than two or three times a second?

Hello,
I am using the Legacy VertexLit shader in Unity.
I am trying to change texture image to simulate TV static, but it seems the maximum material update for this material is only about two to three times a second.

public void Update()
{
....  
material.SetTexture( "_MainTex", someNewTexture);//Set the new texture
...

}

The texture is changed accordingly, but it cannot operate more than three times a second.
Trying to increase the frequency of it to like 10 times a second, still causes the material to change only 2 or thee times a second/
It is a very small texture, 200 pixels by 200 pixels.
I am getting 60 FPS, so FPS is not an issue.

Is there another approach to take?
Thanks

It will change immediately after using SetTexture; there’s no limit on the number of times per second. It’s basically just changing a pointer (not uploading a texture), so it’s essentially instant, and the size of the texture is irrelevant.

–Eric