You can't fix "stupid." Choose one:
1. Stuck for 36 hours without important documents, left behind when evacuating a burning aircraft. (I keep mine in a light vest that I wear, and my German wife has one of those weird little pouches hung around her neck for such items, but that might just be us. It's not so much being poised to flee impending doom with the speed of a thousand startled gazelles, just that some tea-leaf might actually steal whatever we have left in that locker, perhaps while we are sleeping or visiting the toilet.)
2. Being on a slab in the morgue, stone dead because you were stuck on a burning aircraft waiting for someone who needed to take his carry-on baggage, which included important documents.
The same sort of people who ignore the safety briefing don't bother to look for the nearest exit (as they are told to during the briefing that they have ignored), and also don't bother to look at the safety card to see which sort of exits their airplane has ... those are the same people who are going to be stood there fishing their bags out of the lockers instead of focusing on getting down the aisle and off the airplane.
I agree that these "cutesy" briefings (looking at you here, Southwest Airlines) perhaps trivialize something that is important, although the notion is that people shall pay more attention to something told to them in such a light-hearted way, even an important safety briefing.
What we need is segregated seating. One section for those of us 100% focused on surviving an emergency, another for those who shall need to get their carry-on bags, perhaps need to use their phone to record the event for posterity, or do whatever seems to be a good idea, whatever goes through their tiny, unfocused minds once they finally realize that, yes, this is an emergency and never mind what that travel agent promised them. As it is, the problem for the first group is that the second group is going to be in their way, unfair as that is.