While waterproof, that just sounds messy. I can imagine having the "gauze" level pulled out, then you have to dig for the "tape" leve and the wind blows the gauze around (or someone kicks it as they're running around freaking out), then you have to move everything up and out for the C-collar or blanket at the bottom of the kit ...

In a dynamic scene, keeping things organized while secure is a much better plan (IMO). Something like the bucket would be good if you have time/space and a relatively controlled environment.