Does anyone know if having the Chief direct activities has any real effect on the progress or outcome? It doesn't seem to me to do anything--they don't seem to work faster or more efficiently. What's the purpose?

For me it definitely appears to make the progress go quicker and to some extent helps keep the villagers on task.

The chief directing seemed at one point to help one of my villagers who'd so far refused to learn ANY new task, settle into one. I noticed too they tend to progress through the work faster, but it could just be my excitement in wanting to get to the next step, lol.

I think it varies. I had one chief who seemed to make everyone leave the site, the other helped speed things along.