Having a moment to move your dwellers around the vault could be very useful when being invaded by radroaches. I was low on stimpacks at times due to me having some power troubles due to a previous radroach attack. This leaves the dwellers injured without aid except for the slow natural heal that they normally have makes for moments where time is of the essence. Quite a few times i have had it where my dwellers were too busy running around uselessly fighting, making it very hard to click and drag them away. This caused multiple deaths that could have been avoided if the dwellers would sit STILL and allow you to click and drag them into a different room, hence the pause feature.