Do you ever eat the flowers, Sharon? That's one way to slow down their reproduction.
The pistil (the greenish white column in the center of the flower) is the best part, but the flower petals are edible, too. The petals have a hint of a soapy taste but, if your palate is geared towards wild fruit, you would probably enjoy them. In this part of the world, people used to pickle the pistils, like tiny cucumbers, but I don't know of anyone who still does it.
Yucca glauca is the native species here, but Yucca filamentosa is commonly grown as a landscape plant and has escaped from cultivation in southeast Nebraska.