It makes good sense to me -- if we're trying to move a piano from you to
me then either you can push or your end or I can pull on my end: we're
operating on different ends of it, but the effect in both cases is
moving in one direction.
As a mnemonic for remembering which side push/pull operate on, I agree. (A stalled car etc.) It would be nice if the corresponding functions could similarly be opposed without the potential confusion for beginners, but I realize that may not be possible, and your example is at least convincing that it's better than shift/unshift.