The roots of the Santa Claus tradition are tangled and diverse, so it is always difficult to sort these things out. Zwarte Piet - Black Pete or some similar character is often seen in various cultures as the counterpart of the nice old man who brings gifts during Yule. This antithesis to the good is meant to scare children into good behavior, and his antics are also humorous; he draws on many of the characteristics of the European trickster. The emphasis here, however, is on being dirty, unclean, and threatening.

Some see a racist tone to this tradition, but that said, we can see in a lump of coal, something that is dirty to touch. It also has the capacity of igniting and burning for a long time with intense heat, perhaps recalling the fires of hell. I don't see this as having anything to do with work - the direction of your question. A single lump of coal has little worth, it is dirty, and it recalls hell. In the tangle of those ideas, I think we can see why the object given to bad children is coal rather than, say, a brick.