Add "Move to different category" for individual products in Category Manager

I manage a storefront with over 55,000 products and sometimes there are errors in which categories products are assigned to because of errors or inadequate information in the CSVs provided by manufacturers.

It would be great if you could select which categories a product is assigned to right from the drag and drop product manager in the new category tools.

Currently this requires opening up the product itself in a new window and editing/re-saving, which can be very time consuming if you have a lot of products.