I think burst mode is great for all of the reasons listed. However, in my opinion, it is not needed for things that are static or subjects (e.g. waterfalls using ND filters) where I am intentionally using a longer exposure and want the movement or blur. But, when I am shooting people or animals, etc., that might move and I am afraid of not getting the shot I want, then I use it.
One additional point I would add that I shoot a lot of wide angle shots (street, groups, etc.) and in that situation I am dealing with the fact that I do not see everyting the lens is capturing. Also, since I do not have control of the environment things like people moving, gusts of wind, a bird flying, or something else might affect the shot so having a few to choose from is a reat option.
In terms of culling, I do it after every shoot over a coffee and it takes very little time.
Obvious other point: battery life!