'Blowsy' is not really a quality I admire in flowers. Nonetheless the double flowered form of Soapwort (Saponaria officinalis) is what you might call blowsy (in a good way). And it's a plant with a purpose. Rubbing the leaves with water lathers up to produce a thin detergent which was used among other things for cleaning wool and fabric.
Rarely planted these days. These are at the music school which was originally a country villa built for the botanical pharmacist William Ransom in the nineteenth century. Perhaps the remnant of a practical usage? They grow next to an outbuilding which has the look of a washhouse/laundry.