The issue with copying pages to a new site with ACF fields stems from the fact that ACF only stores the ID value of the image in image and gallery fields. Other fields that store relationships are also the same, storing only the post ID. The problem is that when an image is copied it probably does not have the same post ID as the site it was copied from.
The shared media plugin would need to maintain the correct post ID when copying media across sites and I doubt this would be possible.
Most plugins/tools that copy content just copy meta as is. It would be practically impossible to update the ACF values during a copy process of this nature. The steps involved would mean building a custom copy tool specifically designed to work with ACF fields.
The only work-a-round I can think of for this would be to use WP All Export/Import with ACF add on. Export the post from one site and import it into the other site. I’m just not sure how images if images in content would be handled correctly.
