Shoulder dystocia is NOT fun-for mom, or for baby.
If they are inducing early because of concerns that the baby is big-then they really need to do some measuring via ultrasound-and do it often near the end. The weight "guesstimate" calculations that they do with the ultrasounds can go about a pound either way in weight...but the calculations that they do to judge the "frame" of the baby are more accurate.
Basically, if the baby is 8-12 pounds of "chubby" you can have it naturally without too much issue...but a baby with a larger than normal bone frame is where the problems can begin. Fat can smoosh its way through...but huge shoulders cannot. My kids are not only big pound-wise, but big framewise as well...and their calculations that my son (induced at 36 weeks) had a 15" head were DEAD on. Both my kids had a 15" head and chest.
My son was only induced at 36 weeks because they guessed him with a 15" head, and about 9 pounds at that time-a couple days later he was 9lbs, 4oz with the 15" head. At the time, they were trying to avoid a c-section apparently-so they chose to induce early. He could have been around 11 pounds at my due date.
With this baby, I am leaning more towards a c-section, once I am near the end and they have looked at the baby's size a few times. I would honestly, rather have a c-section at about 38 weeks, rather than be induced and birth vaginally at 36 weeks. At this critical time in the pregnancy, 2 weeks can do a TON for the baby's final lung development.
I suggest that you talk with your doctor about measuring the baby's frame-head, shoulders, etc. via ultrasound more than the poundage...REQUEST this before you agree to be induced.
Honestly-I don't see inducing at 39 weeks doing a whole lot. At that point, the baby is putting on about 1/2 pound a week in fat...but the basic frame size is already there at that time. So, I say either induce earlier at 37-38 weeks...or not at all and let you go when your body is ready.