—the way he would utter the remembrances that have been authentically passed down from him.

Those later scholars who deemed collective supplication desirable after the obligatory prayers possess no Sunnah to support them other than the general principle that supplication itself is legislated and that prayers concluded are times when petitions are more likely to be answered. Yet the Lawgiver has already placed this very consideration inside the prayer itself: making duʿāʾ at its close—before one exits it—is explicitly legislated by the mass-transmitted Sunnah and by the unanimous agreement of the Muslims. At that moment the worshipper is in confidential discourse with his Lord, so supplication befits his state. Once he turns to the people, however, that moment is no longer one of intimate entreaty; it is a time for remembering Allah and praising Him. ⦗End of summary⦘

Another benefit
Building on the stronger view that supplication after the salām is not legislated, it likewise becomes clear that raising the hands at that point is also not prescribed. Raising the hands while supplicating in other circumstances, however, is established by sound reports. Shaykh al-Islam Ibn Taymiyyah said: “As for the Prophet ﷺ raising his hands in supplication, there are many authentic hadiths on the matter.” Al-Bukhārī recorded a number of these traditions in his work al-Adab al-Mufrad. Al-Ṣanʿānī added: “It is authentically reported that the Prophet ﷺ raised his hands during the prayer for rain, during the pilgrimage, and on other occasions. The hadith, ‘Allah is too shy to let a servant raise his hands to Him and then return them disappointed,’ likewise proves beyond doubt the legitimacy of raising the hands while making duʿāʾ.”