I agree with @style_wise   these films sometimes take months or years to film as editing must take up most of that time .

I disagree that films do not show the whole chase from a distance. 

Not all animal documentaries may do,  as the actual catch and tearing apart of a live animal is not  'everyone's cup of tea'  so some programmes may not wish to show this , and  they focus on the beauty of the animal, so those expensive lenses are worth the money showing us these beautiful animals in close ups that most none of us can ever experience.