But the ocean will be the ocean and they are paying higher taxes for a fix right now.
Sorry, but beach nourishment isn't a fix. It's a patch. It's a patch that lasts 1-5 years, and really has little effect on the danger to homes on the ocean.
What nourishment is designed to do is to extend the beach out into the ocean. Without that beach, we'd have no tourists. A deep beach that rises gently also has some effect on the roughness/force of the waves, which is important for preservation of the dunes. But make no mistake, it's ultimately dunes that protect the oceanfront homes, not the beach itself unless you're really far back, as the Rodanthe houses once were.
Sometimes nourishment uses part of the sand to build up the front of the dunes. But the ocean doesn't have to go over the top of the dunes to cause damage. If it undercuts the dunes, it will take them out completely. To provide good protection, dunes need to be engineered.
The last go round on rebuilding the dunes in Kitty Hawk has been very successful because they're not just sand. The base of the dunes are bladders full of sand and rocks, so they don't get undercut.
If you notice the photos from Rodanthe, the houses that the ocean took were not protected by anything. In the photo you provide, the gaps in the dunes indicate overwash and under-cutting. Hard to say how much vegetation was growing on them. Not enough obviously.