bball coaches are more visible to the crowd (indoors, confined to one space) and are actively involved in the athletic competition (they can call time outs, make substitutions, receive technical fouls, etc.) They are also only directing 5 players on the court at one time, so the relative role they play is enhanced over other sports such as football.
Bball coaches have more interaction with referees, and a suit helps them appear as more respectful.
Plus they sweat a ton during games, being emotionally and physically involved (standing, pacing) in a warm indoor arena. The jacket helps hide the sweat soaked shirt underneath.
Spectators do not pay any attention to track coaches