There's another confounding factor regarding celiac diagnosis, though its impact may be negligible: the lack of unique treatment options.

I know someone who learned through an elimination diet that they are sensitive to gluten. Maybe they actually have celiac disease, but they currently have no reason to investigate further -- the only practical "treatment" is avoiding gluten, which they are already now doing.

Furthermore, apparently the blood test for celiac disease requires the patient be exposed to gluten for some time before the blood is drawn. So they'd have to start eating gluten again (and thus suffering) to learn whether what they have is celiac disease.

Yes, that is a big problem. IIRC, it's estimated only 20% of people with celiac are actually diagnosed.