Thus far there are no tags for "arthritis", "carpal tunnel", or any other common wrist problems. What is the proposed tagging system here? A general 'catch-all' tag for "wrist problems"? Catch-all tag for "auto-immune" and "nerve problems"? Or individual tags for individual conditions?
I don't think catch-all tags are good in most cases. Obviously it depends on how broad the bigger tag is. For example, the milk tag was removed as the dairy tag (its parent) was not very broad. The general rule for tags is that they should be able to be used alone. I think for many medical conditions, this will be the case, even though you probably will add extra tags to go along. For example, carpal-tunnel-syndrome could probably be used alone, but you would still add in other "helper" tags. Same thing with an arthritis tag. We can see examples of this in many successful SE communities, like SO. StackOverflow has a python, but it also has more specialized tags like python-2.7 and python-3.x.
As long as the parent tag is broad enough and the specialized tag could stand alone, then it is fine to create them. In fact, the specialized tags could help with SEO (search engine optimization).
I would disagree on a general catch all tag as they make it hard to get the information you need. Is your wrist problem a strain? is it broken? is it carpel tunnel? I think they would be better served by a combination of tags that help describe the problem. Could use wrist and arthritis for example or wrist and strain to accurately describe the problem.