Bake wireframe texture with control over line width?

Is it possible to bake the wireframe onto a texture? I’ve seen two solutions so far, using the Wireframe Node in the shader editor or exporting the UV map. Of course the wireframe node only renders triangles… why.

I need more artistic control, mainly line width. Line blur would be nice as well.

Edit: What about creating a wireframe mesh and baking the difference between the meshes or the intersection or the proximity or something? Is there any way to bake a mesh onto another mesh’s texture?