I think most people use boxes just to simplify the storage of their cigars. Also, keeping the cigars in the original boxes allows you to remember what they are and maybe when you got them (e.g., in the case of CC's there are box codes and dates on the boxes; not sure how many NC manufacturers do this). The cedar in these boxes may add to the flavor of a cigar if it is stored (aged) for a long period of time. Not sure that there is any value to the cardboard boxes othen than what I stated above.
I am not sure what you are referring to regarding plastic vacuum bags. I know some people put their cigars in 1, 3 or five "finger" bags -- Ziploc-like bags that have slots (fingers) for cigar storage.
I know alot of people that use five finger bags for safe storage during travels as they are very good at protecting your cigars. Some people also use these in their humidor -- both opened and closed. If the bags are in my humidor they are open.
Just my