Men stepped up their game in the 1920's in order to fit the crime style of the time. Fashion actually evolved from the suit and tie to something a little better.
Since Cars were newest innovation in american society, there had to be a certain look while driving one. When driving, men where usually donned with flat wool hats, leather driving gloves, oxford pants, a white button down with a vest.
Men now could ditch the top hats and go for the more stylish options. The fedora and the panama where the most popular among gangsters,