lacisrmma “Folding the talis under reduces the slipping off the shoulder.”
My husband, a talmid of the Rosh Yeshiva, heard that Rav Hutner z”l adopted this minhag (of folding talis under shoulder) from the Lubavitcher Rebbe (who also folds that way talis on his shoulder) – whom the Rosh Yeshiva learned with b’chavrusa from when Rabbi Schnnerson arrived to America till he became Rebbe. It has to do with kabbalistic “hiding” the black stripes of talis (gevurah) and only exposing the white part of talis (chesed) on the shoulder of the mispallel by tucking them under.
As this shows, that even “mundane” hanhogas of gedolim have deeper reasons (of which few of us ever knew). It also shows the gadlus of the Rosh Yeshiva to be “open” to be mekabel hanhogos from others (even kabbalistic ones), his great respect for other gedolim (even those he sometimes criticized – he refused to permit his talmidim to attend farbrengens at Lubavitch).