No, I've not heard of that. About the closest thing was our HS coach did talk with each player at the beginning of the season telling them what was likely for them in terms of playing time.
So to your question...should a HS level have a depth chart? Actually I think its a pretty good idea. I think a "new" coach would have a hard time implementing it in our area (too many "entitled" parents who would begin the argument with the coach from Day-1)...but I always thought it was good to know where you stand whether in baseball or in your job.
Geez, I think it would motivate me if I saw myself slipping or rising.