Considering that halachah has been around for a few thousand years or so, it is odd that it took a few thousand years minus 120 to establish that one should wear a hat and jacket when davening.
If the earliest psak on this issue is from תר”ע, then it is a recommendation for the population in eastern Europe and nothing more. To call it a halachah L’doros, בכל מקום ובכל זמן is a bizayon to real halachos. A little serious research into halachah would help here.
The American Yeshivish Bubble is fairly adamant that their way of dress is the only viable way. I suggest that these boys spend some time at the Koisel in Yerushalayim, stand in the back and view the numerous varieties of bona-fide God-fearing Jews who come there to daven. The variations in dress are impressive. Interestingly, the American yeshiva boy there stands out from the crowd like a sore thumb. Is his way the only way? Maybe it is on the corner of 14th St. and Laurelwood Ave. but wake up children, that location is not the epicenter of Judaism.
As an aside, there is a book by Rav Professor Eric Zimmer, עולם כמנהגו נוהג , where he traces the history of head covering. It is clear that before the period of the acharonim, head covering was for chachamim only. To extrapolate from the Rambam that all must wear a Borsalino during davening is foolish. Apologies that the book is in Hebrew, so it’s only for the halachically literate.