These kinds of challenges in the street, under the gaze of the masses, are the most forthright and the most public. The parties involved basically have no chance to avoid battle. Anyone who avoids a fight under these circumstances would really never be able to mix in the Worldly Society again; they'd have a worse reputation than Sect Hierarch Xue.
Although this was the most spirited way in keeping with Martial Arts, and every Martial Artist greatly admired it—when Cui Yuanyong went to Beimang to challenge Yue Hongling, it was exactly this way, and Yue Hongling was full of praise for him.
But the Worldly Society is, after all, full of human relationships and worldly wisdom. Generally speaking, if the two parties are familiar with each other, they will not choose such an irreversible approach. If they want to contest in martial arts, they can privately send an invitation, and win or lose without losing face.