The problem is that the badges are added with an overlay on top of the div where the images are displayed. So regardless of the images being displayed, the variants one or the main one, the badges are always displayed on the product page.
It won't be easy to do and that will also add complexity to the loading of the data of the badges. I'm not sure we want to do that. We'll need more feedback from other users to see if there is really a need for it.
I would recommend to do different products in such cases for now.