Not a bad suggestion, I might ask them if I can submit such a statement if they call me to say they can't approve my application.
But there might be cases where it's not about debilitating anxiety or mere inconvenience. What if a person does know eligible guarantors but none of them agrees to act as a guarantor, whatever their reasons may be (even if they are fully aware that the role doesn't entail vouching for the applicant's character, past or suitability)? How is it not a denial of a fundamental right to be refused a passport then if an applicant has tried to persuade every eligible person they know and still could not find one willing to be their guarantor?
To give a somewhat dry answer:
-reasonable requirements for getting a passport are not a denial of rights. (As with almost any other administrative procedure - you can have a 'right' to health care or whatever, but asking you to demonstrate you have that right is not unreasonable).
-It will be VERY hard to show that you are being refused a right if you're not also demonstrating that you simply cannot meet those reasonable requirements. Discomfort and inconvenience is not a denial of rights.
The onus is actually on the applicant most of the time to show they have such a right. In case of a dispute about whether they met the requirements (proof of that right), normal timeframes go out the window.
So unfortunately, the most likely scenario is not that you get refused, but it takes MUCH longer to get your passport than you would like - nope, not a denial of rights. Yes, you can use the 'no guarantor' procedure - and if that (normally) takes two years because applicants aren't meeting reasonable requirements, then ... suck eggs. (Not a legal term)
Proving the requirements are not unreasonable - almost impssibile UNLESS you show some reason you deserve some additional facility.
Which leads to the big exception to my simple version above: the government should not discriminate on the basis of eg disabilities. Show you have a disability - a medical/psychological condition - you have an argument that will PROBABLY be listened to. At least you'll get the benefit of the doubt. Probably . (But you don't want to have to go to court for it - it'll just take a long time and cost you money).
[I am not going to get into whether eg Asp / autism spectrum or some other specific condition meets those standards - not a lawyer, not a specialist. And I don't think going to coourt helps many people, at least in their specific cases. But believe me, I THINK a lot of government employees, including some lawyers, will at least think about it. They will not give a lot of consideration (IMO) to a general complaint of "It made me uncomfortable."]