--a lot of the people who are celiac or gluten sensitive anecdotally report that going gluten free doesn't always improve their neuropathy symptoms.

Some report improvement, but many don't. In the latter cases, it's often unclear whether there is something else contributing to the neuropathy, such as nutrient deficiencies that remain unaddressed, or whether there is simply too much damage by then.

Still, it makes sense to ban gluten from the diet merely to stop the autoimmune assault on the villi, if nothing else. Those do seem to recover in time, though often it's a long process.