I've never cut mine back other than the spent bloom so they don't set seed pods. The foliage stays clean for the rest of the season and I'll cut them down when I do my fall clean up. However, mine are in hoops which keeps the foliage upright and nicely contained.

But if one cuts peonies for floral arrangements, etc - I cannot imagine cutting back some of the foliage as well would do great harm.

Definitely do not cut them down completely. Not only will that weaken the plant which uses its leaves all summer to store energy for next year, but some peonies turn nice colors in the fall.

If the plant is large, healthy, and well-established, you could shorten it a bit with no harm done. Younger plants need all their leaves.

On my huge plants, I cut off the flower stalks by reaching down below the rest of the foliage, so the stumps don't stick up above the bushy mass. My plants are also in hoops, so they stay upright, but it is not too late to tie them up loosely with string. Without the flowers to get wet and heavy and topple over, it doesn't take much support to keep the stems upright and they will look better.

I'm very fond of how busy and green my peonies are after they've bloomed. Unless they get all mildewy, they are wonderfully lush until...well, now, fall. I leave them gently fenced up so they don't get too floppy.