I divided Singing in the Rain, Strawberry Blonde and Berry Garcia last weekend and all I can say is have a saw ready! It was like sawing through hardwood. Mine were in place for around 6 years but they were planted as 4-6" pots.
You see lots of people advising not to plant back in the same spot but I always have. I normally divide, put part back in the same place then plant the rest elsewhere. I do replace part of the soil with some planter's mix, though. I've never had a problem but CO doesn't have a lot of the problems peonies have elsewhere because it's so dry here.
As far as what will happen if you don't, you'll probably just end up with a very large, very pretty plant! I've never heard that Itohs have to be divided, just if you're going to do it not to let the roots get ginormous, they're a LOT harder to divide than a herbaceous. There are some herbaceous peonies that will start dying out from the middle if they're left in place too long but I don't think Bartzella should have that problem. Hopefully someone else will answer you that has had one in place long enough to get really big! Good luck!

Were the ones you divided still blooming well?
Mine came from the peony sale in KC, Mo It really wasn't all that big at the time of planting.
I think it will take at least 3 people to lift it out of the hole.

Yes, mine were blooming well. Good luck with your monster sized peony root!