Convex MeshCollider Doesn't Work on 2D Plane

I've created a mesh in Blender that is just a 2D plane made up of about 6 or 7 vertices. When I import it into Unity and use it as the source Mesh on a MeshCollider, it looks fine. But if I check the "Convex" box on the collider (because my plane is convex), Unity turns it into a much large box. If I extrude the shape in Blender and give it some depth then it turns out okay in Unity when I mark it Convex.

Can you not use the Convex option on 2D meshes, or this just a bug?

Here's the original plane.

And here's the same collider with the Convex box checked.