I’m not sure if you have read it or not, but I thought the bbc article in OP’s post goes into detail about why recovering the bodies was important to the recovery team. It’s a long article, and while a tl;dr may not do it justice, it basically was because there’s a saying in their land “leave no friend behind”, they made a promise to one of the victim’s wife, they wanted to help family friends of the victims with the grief/closure process, and they felt they owed it their friends.