I've run a quick check and haven't really found much in the way of categories for health care facilities and most things related to health care are professions and cemeteries tied to the old "asylums."
I believe adding hospitals needs some discussion.
I do not believe that we need to add hospitals for a short-term visit a (we'd have to add nearly every hospital in every city and the categories would potentially hold thousands) and I see no genealogical need for that. Of course, these things can always be mentioned in the biography without need for category creation. See my own gg-grandmother's profile, as she spent time in a mental health facility:
And if you're adding categories to unlisted profiles of living persons, they will only be seen by people on the trusted list of the profile.