Yeah, Sarah kinda drives me nuts falling over- many years I have cut all the blooms and enjoyed them in the house. It just drives me nuts seeing them flop. She's in full sun and still flops. I may be a good gardener this year and cage them
In fall I planted 'Pink Kisses', that has big fluffy blooms, but is short and has sturdy stems. I also have an old Japanese/Anemone flowered pink peony that I like much better. It has multiple blooms per stem, and they stand even after rain. Floppy Peonies is what lead me to start purchasing some named varieties- and only those that are said to have strong stems or require no support. Another I really want is called Pink Flying Saucers, but it has sold out the last 2 years before I got my order in. I'm also adding a couple they call red, but are hot pink to my eye- Scarlet Ohara was installed in fall.
Singles, semi-doubles, Japanese and anemone types typically are better for standing without staking.