Although the Mishna Berura implies that the requirement to wear a hat for tefillah is societal, Rav Moshe Feinstein ( I didn’t read the teshuvva, so I don’t know why) says that it still applies nowadays. Also, Rav Soloveitchik required atifah for all devarim shebikdusha (with certain exceptions), and he said if you won’t use a tallis, a hat will also suffice.
On the other hand,the Tzitz Eliezer (13:13)says that since nowadays most people have no problem walking in the street without a hat, it is not necessary to daven with a hat.
In yeshivish circles, many people actually tend to walk in the street with hats.
But those who are careful to daven with a hat, and those who don’t, have what to rely upon, as there are poskim who rule both ways.