I do see an advantage to a centered line in that you know no matter where you are, that line marks the ideal center of the timber. I could see a possibility for the occasion of getting lost or confused now and then with an off center line, usually as a matter of error of judgment. With a centered line this is a non issue.
DL, have you ever used square rule for working timber? One of the premises to square rule is knowing which face is where, and having the reference edge/snapped line closer to this best face is not confusing, in fact it makes the system more clear.
So, two advantages to snapping lines off center are highlighting the reference sides and delineating the joinery locations.
I am still not convinced a center line is the best location, perhaps there is an occasional exception. And it can be done without pre leveling of the timber, as has been mentioned, pre leveling is just an extra step as is center lines.
