I seem to recall there was a serious bug in version 1.0 not long after chocobo riding was added where it allowed players to do this very thing (actually mount another player character) - naturally it was most definitely not working as intended and quickly patched, but not before the inevitable memes were generated from it.

As cool as it would be to have as an actual feature, I... shudder to think how a lallafel would handle giving a roegadyn a piggyback (even with your wheelbarrow idea).