This post is a little bit speculative and I apologize for that. But it's based on situations avoided rather than trouble arrived at.
I am extremely interested in the propagation and the expansion of most of the cultivars that I've purchased. As a result, I spent quite a bit time examining the roots that I receive. Occasionally taking a closer look results in action. For instance, I find pieces of the crown that are thin or unlikely to produce stems and feel compelled to cut it out so there is room for new growth.
That said, I've thrice encountered a situation which could poise an enduring problem. Embedded within the tangle of roots and crown, I've found small but independent pieces of a root with an eye or I've found that the tangle was close to 50/50 but truly divided.
One of these is worth describing. I had a large piece of root that I was evaluating for possible division. When I do this, I tend to trace the roots and push or pull on them as I look for a good spot to cut. Well, one of the roots wiggled quite a bit. It was cut on the backside and when I wiggled it, an eye was moving back and forth. I was able to push the root out and ended up planting the single eye root. If I had planted this root intact, I probably would have missed the floating eye and I think that I would have had strong potential for a lasting and fairly invisible problem.
I've read posts here about peonies that aren't performing well and yet have the same advantages as other peonies that are exceling. If you've somehow managed to get two peonies started in the same location, I doubt that the end result will be very good.
Anyhow, I am bringing this up as a cautionary tale. I think that the larger the root, the more important a through examination becomes before you plant it.