Mepla, that was the point. Yeshivish way of dress evolved (or devolved) from the Slabodka standard of dressing in “conservative elegance”, to look like the respected goyim. This elevated the stature of yeshiva bochurim throughout Europe.
Hats and jackets for davening do have halachic basis (how you dress in front of an important person is by wearing a jacket, the hat from kavod or the idea you need a kisui kaved, or a version of ituf with the tallis). That said, sometimes it’s better to let them have little pleasures of rebellion and stave off bigger ones. Ask your LOR of course.