The Shulchan Aruch [91-6] writes that it is the way of chachomim and their students to daven only when they are wearing a jacket. The Kaf Hachayim [91-26] writes that since all people would wear a jacket when meeting with a king, one should do so during tefillah.
So how is it that sometimes certain people don’t wear a jacket by davening (especially Shachris, with no jacket under the talis — but it occurs too frequently even by other tefilos).