I don't know the history behind double boxing and dressing speakers in bags, but I have some answers to your questions. As for the double boxing, I have had to send electronic equipment home for repairs, and those boxes can take a beating during the round trip. So I don't think you really want to get rid of the outer one.

As for the door to hide the nobs, lights and switches, two suggestions. Cables go in there as well. On a sub particularly, you'd probably complain rather loudly if, as it was shaking your house, that door was rattling because it no longer closes tightly or due to environmental conditions shrank a little. You really don't need or want that door.

Subs come in many sizes. If you want a smaller one you can get it. Some people have bigger rooms or want the floor to shake more, so they get bigger subs, or they get 2 bigger subs. If the one you got takes up too much space get a smaller one.

Power cords on audio equipment are short for a reason. They collect radio frequency interference (RFI). If you've ever dealt with it you know its a pain in the (choose your body part). The longer the cord the more of it you can collect and hear. Things that need grounding get it. Things that don't, ... well why add another wire to collect RFI. Gonk and some of the technical types around here can explain this one better than I.

Enjoy your new sub. Maybe you can use Paul Bunyan's pillowcase as a laundry bag.