I found out why my heavy goods were not being transported efficiently. I had one wagon shop and when I checked, the guy had made one wagon in his whole life then got in it and spent the rest of his life driving it. The description needs clarifying then, it did seem to imply any villager could drive one. “A workshop where wagons are manufactured. Villagers can drive wagons…” It should say instead: “A workshop where its workers create and drive one wagon each” and the activity description should say “Building a wagon” not “Building wagons” as that was misleading - the worker will only ever build one.
Also I have noticed they won’t drive one someone else has made. When one of my wainrights died he abandoned his wagon and ran home to die - pretty reasonable really. So then I hired another wainright to take his place, and he insisted on making his own wagon, leaving the dead man’s wagon just stuck in the road.