eBay can earn money by charging fee for this option.
It would benefit a lot to provide choice to buyer to select the shipping company he like to have.
At the time of listing, Seller should be given ability to provide an option for providing different Shipping company names that can be selected by Buyer at the time of his purchase.
ex: We list an item, tell that we can ship only through Aramex, DTDC, Sunami Couriers and respective shipping prices. Then when Buyer comes to this listing and at the time of checkout, he can select from a drop down menu or listmenu that shows only these 3 couriers, he can select any one or more and then pay.
Here, benefit is:
Buyer knows better than Seller about Buyers area and courier service to their area.
Buyer may have DTDC office near to him and so select that one.
Seller is safe that he no need to go to far away courier company to ship the item. Say, if a Buyer location is not served by Maruthi couriers (Sellers regular couriers which is near to him and charges little less), Seller should spend money to goto India Post (unknown courier company to him or never dealt) or will not ship the item at all. Then refund happens, Seller gets paisapay penality.
Manymore benefits of introducing this option, this system is already being implemented by other online ecommerce portals.
Regards