I was talking about the olam who doesn’t wear hats. Obviously they don’t believe that you need a second head covering for davening (and there is basis for that view). Yet some still wear the talis over their head for devarism shebakedushah during Shacharis and others the entire Shacharis, while wearing nothing on their head (other than a kippah) for Minchah and Ma’ariv.
I do this, to honor the Rav of the shule where I grew up and davened until after I married. Although it was a small shule, and not in the main frum area of the city, most of the kids who were brought up there are frum today, across the spectrum – from chareidi to yeshivish to MO. Although I don’t wear a hat, I do cover my head with my talit during most of shacharit – i made it my minhag, to follow the example of that particular Rav.