You guys ever tried carrying folded-up chainmail? That stuff is heavy. It's designed to spread weight evenly over the body, so as heavy and uncomfortable as it is to wear, it's so much worse to try and carry in a bag.
Yes, actually. As mentioned, my brother is part of the SCA and another medieval battling type group, and once or twice I've helped them move equipment. It was very heavy, and very tiring just carrying it once across the length of a football field. And, as mentioned, my brother gave up on wearing chainmail after about half a day at Ren Faire because it was too uncomfortable, and that was just him walking around.
Additionally, chainmail isn't just chainmail. It's also leather or cotton padding to protect you from the chainmail itself (recall that Murph's special chainmail vest is a doubled up kevlar vest). The kind of stuff that can reliably turn aside or stop cuts from something like a ghoul in a fight is going to be thick, heavy, and bulky--meaning it's uncomfortable to wear, uncomfortable to carry around, and is going to take some time to put on and secure properly.
Carrying a sword or an axe in a dufflebag means that when something attacks, you put down the bag, reach in, and yank out the weapon ready to fight. It's
maybe a supplemental action.
Carrying chainmail in a dufflebag means that when something attacks, you're better off just swinging the bag and using
it as a weapon than trying to put it down, reach in, unfold the chainmail, get it over your shoulders and arms, and buckling it on. At the very,
very least it's a full round action, during which you're wide open to declarations like, "Arms Pinned In The Sleaves" or "Can't See Because It's Over My Head" and you're a recumbent waterfowl.