There was never a time when it was usual for managers to wear street clothes in the dugout. The original reason managers wore the uniform was that back then all managers were also players. so a guy would (say) play third base and manage the team during his playing career. Then he retires from playing, but he’s still the manager, so he keeps wearing his old uniform out of habit. There are no more player-managers (the last one was Pete Rose) but by now it’s a tradition. Tradition’s don’t need a reason. Connie Mack, owner and manager of the old Philadelphia Athletics, used to wear a suit and tie in the dugout. As did Dodgers manager Burt Shotton. There’s now a MLB rule stating that no person not wearing a uniform, except medical personnel, is allowed on the field of play during a game.