I think Experience would be ok for the Normal/Good/Great Infantry Commander. However, I like the ideas of traits being "special" but standardized bonuses.
Trait ideas: Defender, Stalwart Defender, Great Defender; Unit can withstand more attack (so increase health of commanded unit by 10/20/30%? Infantry will be 35/38/42, Cavalry will be 30/33/36, Artillery will be 11/12/13). Alternatively, decreases chance of both Retreat and Charge. (actually, might be good for a Disciplined trait, which has a smaller bonus than Speecher, but it is always there).
Driller, Drill Sergeant, Drill Master: Increases speed of formation changes (?). For artillery (column) and cavalry (line), makes actions against the "wrong" formation more successful.
Jogger, Runner, Sprinter: Unit moves faster when Running and effectiveness decreases slower.