Hi!
While it is a great idea, the problem is that taxonomy terms have no images by default in WordPress (as far as I know). So there is no standard way of parsing those images, it varies for every plugin. This fact makes it impossible to implement a feature to select image sources by taxonomy.
I can of course suggest a way to display the term images, but I need to know how they are stored, or how to get them.
For example, I have found different poast support topics for this, and each one has a different resolution based on how the taxonomy term images are stored:
Term images using PODS
Term images using woocommerce term meta
Term images using Featured Images for categories plugin
Another different storage method
This is only the ones I could find in a few minutes, there is much more. As you can see, each and every solution is different, depending on the implementation.
Do you know by any chance how those images are added to the taxonomies? (any plugin used, or a theme method or something else)
If you happen to know the function name to use to get the term images by ID, that would be the jackpot.