The original sense of conveyance was a document that transferred ownership from one person to another. It is interesting that language has shifted the sense from the document to the movement.
Now a conveyance suggests some transportation. Something as still and inert as a piece of paper can become a moving object.
Also – it is quite extraordinary how many pieces of paper, how many documents a person can acquire in his or her life. If you had to take them with you to the grave, there would be no room for you in it.