Aside from the usual reasons given (a plane consisting mostly of steel armor could not get off the ground, etc.) it would make no difference to the passengers. Falling to the ground from altitude will kill you even if you are sitting inside an indestructible box, simply through rapid decceleration.

They do that, but it's not called an "airplane" anymore. I think the usual term is "submarine".

Because it isn't the fall that kills you.

It is the sudden stop at the end.

Too much leg room if they do that

Because it would be too heavy to take off.

then they won't be able to fly. :P that's why we have airplane bodies made out of lighter metals instead of heavy ones used in black box.