as his handling of the matter in his Ṣaḥīḥ indicates, as Ibn Ḥajar records in Fatḥ al-Bārī; he then adds:
“This is the position chosen by Ibn al-Mundhir and Taqī al-Dīn al-Subkī among the Shāfiʿīs.”
The meticulous scholar al-Shawkānī likewise leaned toward it.
As for declaring the prayer invalid merely because one has not wrapped the cloth, the ḥadith does not clearly support such a verdict. Allah knows best.

A further issue arises: if a person is wearing a tight izār (lower garment) that cannot be used for wrapping, is he obliged—when he has the means—to put on a broader one or to add a ridāʾ (upper cloth) that will cover the upper part of his body?
The view that seems correct to me is: yes, he is obliged to do so, contrary to Ibn Ḥazm, who states in al-Muḥallā:
“If it is narrow, he may gird himself with it and that suffices, whether or not he possesses other clothes.”
I say: this is rigid adherence to the literal wording of the ḥadith without regard for its intended meaning, which is to cover the body. The Prophet ﷺ underscored that intent by forbidding a man to pray in trousers without a cloak, as mentioned earlier. Allah knows best.

Concerning the Prophet’s ﷺ own practice of praying in a single garment, he only did so while wrapping himself in it, as explicitly affirmed by a number of Companions: ʿAmr ibn Abī Salamah, Umm Hānī, and Jābir ibn ʿAbd Allāh in the two Ṣaḥīḥs and elsewhere; Abū Saʿīd al-Khudrī in Muslim; Anas in the work of al-Ṭaḥāwī; Kaysān in Ibn Mājah; and many others besides. I have gathered their reports in my book Ṣalāt Rasūl Allāh ﷺ (The Prayer of the Messenger of Allah).