The act of wrapping oneself in the Tallit is an obligation. The Torah Lishmah (Siman 124) wrote that the Tallit should remain on until after Aleinu Leshabeach, as this serves to remember the “Encompassing Light” (Or Makif) that descends from all the upper worlds down to the World of Action (Asiya) through the Tallit. The Bach (Siman 8) wrote that the Tallit must be over the head from the beginning of prayer until the end, as this humbles a person’s heart and brings one to the fear of Heaven. Righteous individuals (Tzadikim) were meticulous to recite even the Morning Blessings (Birchot HaShachar) while wearing Tallit and Tefillin (as noted in Menorat HaZahav from Rabbi Zusha). The Radbaz (Vol. 2, Siman 342) defined this as “the custom of our forefathers.” The Magen Giborim (Siman 91) wrote that even when it is hot, one should not remove the Tallit from the head. The Eliyah Rabbah wrote that one who removes the Tallit from the head is considered as if they have “cast Me [Hashem (God)] behind your back.”