But they are not out of fashion
Fashion is the prevailing style or custom, as in dress or behavior. That is what "fashion" means in English. Braces are out of fashion. Feel free to visit any business area. Chances are 8 out of 10 men you see are not wearing braces. If someone chooses to wear braces, that's fine with me. I
choose not to because I don't like how they look when I'm wearing them. It isn't a matter of them being "classic" or not. There are a lot of "classic" clothes that will definitely look anachronistic in most environments today. Good taste does not mean looking obnoxious, and unfortunately most people today will react to braces as such.