A mattress generally does not have enough rigidity to allow it to be carried by the far ends like that. If you put handles at the head and foot and carried it that way, it would likely sag so badly that you'd be dragging it the whole way.

Edit: Nevermind. It works fine so long as you turn the mattress on its side like everyone does when they actually move a mattress. The diagram made me think of carrying it flat, which really only happens when assembling the bed.