You're on the run anyway, correct?
Three cubic feet of cloth is actually quite a lot, and each otherwise-useless commoner3 gets it for six hours. Normally housing all these people for the night would take a lot of time setting up and tearing down shelter. Similarly, repair your wagons, light fires (3 cubic feet of vegetable oil is a lot; something like 20 gallons) build rope bridges, snare animals, make sterile bandages, disinfect wounds with shortlived wood alcohol, et cetera. Tracking you will get harder when much of the evidence vanishes on its own.
Sure, it isn't the most practical in combat (though you can make some javelins or wooden armor out of it if desperate), but when you're traveling light the ability to say "yeah, we have that" cannot be underestimated.