I still don’t think it would work (except for maybe a very simple version).
The router would be putting a lot of stress on those thin little pieces. The plywood would fail in my opinion in too many places based on grain orientation. It would be an interesting experiment though.
The laser doesn’t require any hold downs during the cutting meaning there is no stress on the wood other than it being vaporized.
Doesn’t mean a cnc router can’t do some cool things a laser can’t do (or not as well).
Note: Grey scale height map images are a form of cnc patterns. They can be converted into 3d geometry with different software. Blender3d is a free program that can be used for this.