Crop command embedding linked images
I would be thankful if linked images remain linked (instead of being embedded after using the crop command). I would like to believe that this can be made possible. This is the normal behaviour in other graphic design software.
If you want to keep a cropped image as a live linked image, you should Clip it instead. Press the Mask button (in Control or Properties panel) and Ai will create and select a rectangular path with the same dimensions. Transform this path with any tool you like or with the bounding box, and the image inside will remain unembedded.
Crop command, on the other hand, is intended specifically for 'physical' cropping, and since Ai won’t edit the original placed image, it gets embedded and then cropped.
Just use the method you need.
Please comment back if it works for you.