I often will remove a section of a peony and leave the rest of the plant. The center of the plant is mostly old growth, not doing much. The outer edges is the new vibrant growing part and easy to just cut off a section to start new plants. I do not find digging up the whole necessary. Al

I see no reason not to plant in the same spot if your peonies are healthy. They say that to prevent spread of disease..the same reason we're advised to dip our clippers in bleach solution between plants, and putting cuttings in trash, not compost.
I've divided & replanted with good results.
Good luck
Heather