Webbing slings are used in material handling industry the most. For example, webbing slings have replaced chain/wire ropes previously used for lifting of heavy equipment. The advantage of webbing slings is that its width is more than chain/wire rope which distributes the reaction force on the object being lifted thereby reducing the damages. These slings have highly reduced the damages on steel coils (as shown below)

They are also easier for handling and generally weight just 20% to 30% of a wire rope sling of equivalent capacity. They are also cheaper than manufacturing of chain or wire ropes.

Another advantage of this material is its low elongation property. This makes it suitable for use in lifting/lashing. A webbing sling generally has an elongation as low as 3% to 7% under load. This makes handling of heavy equipment/object easier for the crane operators.Polyester Flat Webbing Sling  Factory

The low elongation and high strength have also found an application in lashing of cars.

These orange straps that you see are sufficient to hold the car in position for its entire journey across the ocean. Before these belts, big wooden wedges had to be nailed all across the car to secure it. Thereby saving nature as well.