I actively encourage my teams to record Near Misses (in a manufacturing environment) as it would allow me or the Safety guys take precautionary steps before a major accident occurred.
I believe that the more Near Misses that are recorded, the more chance you have to prevent serious damage to individuals in the future.
Near Misses are a target I measure against - I measure the decline of incidents relating to body parts that have Near Misses reported. This shows me that the effort of reporting Near Misses is useful.