'This should only be a last resort' is a downright terrible way to explain this to people who are in this situation.
If it isn't a last resort not to wear one, then you're not really experiencing "extreme distress"?
You are exempt if you
cannot wear one due to those reasons, not because you find it mildly unpleasant, as I expect everyone does - I do.
Before deciding to take an exemption you really should try different ones (the face-shaped fabric ones I find much less unpleasant than the single use medical ones, for instance) and see if there's a way to wear one (or a visor, in England) before taking the exemption as - a last resort.
There is a list of valid reasons for not wearing one. Nowhere in the legislation does it say that you should try your best to wear one even if you have a valid reason not to.
You only have an exemption if you
cannot wear one
and you have one of the situations listed. You aren't meant to just say "I have asthma, I'm not wearing one", for example (and Asthma UK have led the way in pointing that out - some asthmatics will find they cause a breathing problem, some won't, and there's only one way to know unless your doctor has explicitly told you not to) - it actually has to be that it will cause you a genuine problem. You can't really know that without putting one on at least once to see if it does!
And "extreme distress" is not "mild dislike or discomfort". It's something really serious - think phobia level. There would seem to be a few such people on here (
@Scrotnig I figure I wouldn't be out of order in saying you would experience "extreme distress" if you had to wear one?), but not everyone who just dislikes the idea.
(this is getting a bit like the old adage of "how do you know you don't like food X if you've never had it?")