Is it permissible to pray supererogatory prayers while walking to fulfill a need, by analogy with the abundant prayers of the Companions and the Successors?

The supererogatory prayer (Nafl) for a resident while walking is not permissible because it involves many actions that contradict the prayer, such as failing to face the Qibla. However, for a traveler, performing supererogatory prayers while walking is permissible according to some scholars. The Shafi'is and Hanbalis have cited the permissibility of this, analogizing it to one riding. Some have gone further, stating that facing the Qibla is obligatory at the beginning of the prayer, and then the worshipper may turn in the direction of their travel. It is also permissible for a traveler to perform supererogatory prayers in a vehicle, due to the confirmed practice of the Prophet, peace be upon him, in doing so.