We are using TechShip to accomplish this with Shopify carts.

We appreciate the feedback as well as another member of the community mentioning their solution.

Connecting rate shopping directly to Shopify via intergration would certainly be possible but not without extensive development based on how it currently functions.

The Shipedge integration with Shopify imports data once the order is created/processed however prior to that there is not currently a way for Shipedge to see the details of the order such that it could generate a rate.

While this won't be something we pursue at this time, we'll keep the feedback here for consideration in future improvements to the Shopify integration.