Ask Mr. Smarty Plants

Instead of being visited by damaging flying insects on your Yucca flaccida (weak-leaf yucca), we believe the flowers are being pollinated by the yucca moth partnered by genetics with that precise yucca plant. Here is a very good article from the  USDA Forest Service on Yucca moths. According to this article, at some point in the history of the moth-yucca co-dependence, the moth may have actually been feeding on the blooms.

When you see flying insects around your yucca, they are most likely females selecting a place to deposit their eggs, which is in the seed pod. She collects pollen and then pollinates the flower. When the larvae hatch, they feed on the seeds in the fruit. The mature yucca moth eats nothing, because they have only a few days to live. Please don't spray any pesticides around that yucca, because you will interrupt a very important process in your yucca. After the blooms have all gone and the fruit has dried, the fruit will open and the seeds will be ready to move to a place to grow a new plant.

Working  at the Lady Bird Johnson Wildflower Center on cleaning Texas native plant seeds to send to the Millennium Seed Bank, we have cleaned the dried fruits of yuccas to obtain seeds for the Seed Bank. Many of these seeds had little round holes in them, rendering them sterile, of course. This was the results of the larvae feeding; in fact, we sometimes chanced on a larva that had not yet left the nest. The yucca has adjusted to not allow all its seeds to be eaten by producing a LOT of seeds. Here are some pictures of the yucca moth.

Pictures of the yucca moth from Google 

Pictures of Yucca flaccida (weak-leaf yucca) from Google