Light bag workout provides benefits to improve various aspects of kicks and punches. It provides a good coverage of speed, mobility, power.
While hitting a light bag, the weight of the bag demands that the hits are quick and snappy, because 'pushes' as opposed to 'hits' fail miserably on light targets, highlighting the sensation of wrongness when throwing a strike that turns out to be a 'push'. The extreme of developing this 'snappiness' is to use a very light target such as a focus pad, or a piece of paper on a string. So hitting a light target demands that speed of delivery and balance on recovery are key.
The light bag also provides enough resistance to strike realistically heavy hits. Landing heavy hits is fun, and when done in a fight, will cause a knockout. But most of the bout is sent throwing hits that make light contact, miss, are parried or blocked. Landing heavy hits on a heavy bag does improve focused strength of the hit, but if not careful, hitting a heavy bag can result in 'pushes' being thrown. With a light bag, heavier hits with all available strength can still be performed at opportune times. When a swigging bag is coming back, strike on an opposite angle to its direction of travel can be done with full power and appropriate resistance would be supplied by the swinging bag.
The variety of techniques and skills involved in a light bag workout provide training of skills utilised in a sparring situation. It provides, 'middle ground' between the fragmented extremes of very light and very heavy target practice.
My videos below illustrate the use of light bag workout for kicks and punches, then just kicks.

What do you think about these points, what's your favourite weight of the things you punch and kick?