Even very simple Blender model kills my framerate on iPad

I have a very low framerate when even the most simple Blender model fills the screen.

Here is what I did to recreate the problem in the most basic use case:

Create a new scene in Blender, delete camera and lamp, create a plane. Make the dimensions 100 in x and y, choose "Scale to Object Data". Save.

Create a new project in Unity. Import the plane from Blender. Make sure scale is set to 1 in the game object. Rotate the plane and move it so it is in front of the camera and fills almost all of the screen.

Attach a script from the Wiki to the camera that logs FPS to the console.

Build on the iPad.

The framerate drops from 59 fps (when I hide the plane and set kFPS to 60) to 20 fps when the plane is shown.

The plane consists of two triangles. I have that problem with all models imported from Blender. What am I doing wrong?

I have found the cause to be the default Diffuse material applied to the object. The problem is the same as described in this question.