I have spent more than 30 years doing a great deal of out door work and I have found a hundred uses for a bandana, including as a mask, for dust though. I do not think it would help much in a chemical contamination situation. You are right that it is easy to improvise, but it always seems that if you don't bring it, you won't have it. A bandana takes up little room and weighs almost nothing. I generally use a triangular bandage as a bandana, but I do like to have a larger one at times.

Just talking about scenarios where there is contamination, I have experimented with a clear plastic bag. If you have clean air to fill it with, you can put it over your head and breath safely for more than a minute, keeping a tight seal around your neck. I know how this sounds, but I tried it and it works for a short time. Maybe enough to escape to a safer environment.