Even on courses with wide, expansive fairways, its not uncommon to see features such as bunkers and mounding that create a more natural bottleneck to the entrance of the green. It would seem that overtime the grass lines were brought in to mimic the presence of these features, creating a similar challenge to a running ball trying to reach the green, without the feature needing to be present.
At the same time, as the game evolved to be more aerial focused, the bottleneck acted as a buffer for poorly hit aerial shots. A player expecting to fly the ball all the way to the green would be unlikely to find a miss hit shot landing short and bouncing up onto the green.
As bunker shapes and mowing lines became simplified during the post-war era, the bottleneck presented both a visual separation between the fairway and the green complex, while also acting as a type of hazard within a more aerial focused game.