If done properly, paper tuning would require exactly the same amount of trial and error and be every bit as much of a pain as bareshafting. Very few people do it properly though.
No point in me going into the how-to part of bareshafting. Black Frog' s got it hammered.
As for bare shafts kicking one way or another in the target, sometimes it' s the tune and sometimes it' s the target. Without fletchings steering the arrow straight, the point can drift off into a softer part of the target. Even if it' s initial contact was straight on, the shaft will be sticking crooked in the target.