Maybe Elimination Diet testing is adequate to reveal gluten & wheat sensitivities but I kinda doubt it.
I agree that having a gluten/gliadin allergy or intolerance can have dramatic effect on a person's health. Often removing wheat from one's diet can result in dramatic improvement.
Blood testing for gluten sensitivity, if I remember correctly, is done with a tissue transglutaminase test. I think that means they're looking for the presence of a particular enzyme. The test works really well for identifying Celiac's disease, but it's not definitive for mere gluten sensitivity.