The problem is that such a list is impossible to police. I fall into one of those categories (in practice I would wear a face covering if I had to travel, to avoid conflict). But you wouldn't be able to tell just by looking at me - even most people who know me well wouldn't realise I was eligible. Would a driver let me on without having one on? Probably not - I wouldn't be able to prove eligibility!
Like with quarantine, if you have a list of excuses as long as your arm the whole thing is worthless.
The intent is clearly "if all available designs of mask cause you a serious physical or mental health problem AND your condition is in the list, you can be excepted". What will happen, as ever, is that people who just don't like the idea will use that list as a means of not bothering.
To slightly misquote Matt Hancock, it's now your civic duty to wear one unless you
absolutely can't.
For instance, they will not be an issue to all asthmatics. You should, as an asthmatic, only claim the exception if it will cause
you to have breathing difficulties. Asthma is a huge continuum, from people for whom it's barely noticeable day to day and it just feels like being a bit unfit (e.g. me), to people who can barely get out of their chair without their oxygen level falling dangerously. Clearly the need for an exception tends towards the latter, not the former.