Nether River had long cultivated the Xuan Yuan Water Control Flag to unparalleled purity; if Yuan Hong had tried to snatch it with his Innate Divine Ability directly, it likely wouldn't have worked. Striking it once with the Cornucopia, however, was almost guaranteed success. Once he got hold of it and threw it into the Cornucopia, even Nether River with his tremendous abilities couldn't reclaim it.
Moreover, in this battle between Buddhist Sect and demons, the Green Lotus Treasure Flag had actually been taken back in advance by Amitabha Buddha. It seems that Amitabha Buddha also knew that if he didn't take it back, it would have been seized by Wukong. There was no use leaving the Green Lotus Treasure Flag behind, as it could not salvage the defeat of the Buddhist Sect. Why should he simply hand it over to Wukong?
