This is my instinct. I just find the alarming insistence on the Coeliac UK website a little bit disconcerting!
My understanding (limited so far) is that the reason to get a diagnosis would be to get the automatic screening prog that coeliacs are offered - which I think includes yearly bone density screening and possibly screening for crohns and bowel cancer. you can also get gluten free nasty baked stuff free on prescription if you are diagnosed but I wouldn't want that anyway. Both the diagnosis and the screenings would be free on the NHS.
TBH as an EDSer with known allergies already and with a very friendly, sympathetic and open-minded GP (she needs cloning!) who is happy to read things I give her and google and admit she might not know, and has bent certain protocols for me in the past anyway, I suspect she might be able to let me have the bone density and bowel cancer screenings anyway.
I might be inclined to do a scheduled, planned challenge with certified gluten free oats at some point, just to know for sure (whether it is all oats, or just gluten-contamimated ones). But not before my holiday!
We have recently taken my elder daughter off grains as she was having constipation and she is so much less moody and difficult without them. My younger daughter still gets sourdough rye bread if she asks for it (but we don't offer) because I want them to come with me of their own accord, not by force. I am now wondering whether I have done my daughter a disservice by taking her off gluten before getting her tested, but it would be too horrible for her to start eating them again. She would be really distressed at the thought of it - she is only 5 but she's really good at asking if anything she is offered is safe. She hated the constipation so much and has been clear of it since giving up grains and she's a sensible girl who would rather feel well than eat bread. I don't think I'd want to put her through that. She is an EDSer too.
We both used to have milk allergies, but by avoiding triggers and nurturing our gut a bit we managed (after a few years) to outgrow them and we can both now have hard cheese and butter (though I personally only eat unpasteurised cheese).
My husband and youngest daughter don't have any of these issues, but he is primal and she is mostly primal (occasional sourdough excepted).
Sorry - rambling now! Thinking aloud!