As chemistry and the other science disciplines become more interdisciplinary and research often no long fits into neat boxes that we can label as "analytical chemistry", "physics", "molecular biology", etc., it seems odd to me to recieve a PhD in chemistry for research that spans the disciplines of computer science-molecular biology-physical chemistry-spectroscopy-analytical chemistry-(I could go on). It would be more appropriate to recieve a PhD in science it seems, but odd too to describe increasingly focused detailed research in even more general terms.
Does what you recieve your PhD in really matter any more? Should it be generalized to just science? Why or why not?
If you plan on going into research/industry, a PhD in science is fine and makes sense, as you pointed out. However, if you plan on going into academia, it gets a bit fuzzy. Accreditating bodies look for faculty members that have a degree in the field they are teaching. The second (and seemingly less preferred option) is to have 18 graduate hours minimum not incuding seminar, research and dissertation in that field. So, if someone wishes to teach at the post-secondary level, they need to be aware of this restriction/criterion as do graduate advisors.
I think it all depends on what you intend to do with your Ph.D. and what potential employers might (or might not) be looking for in your background. Most employers are looking for a specific knowledge-base when they are considering a candidate, and having a Ph.D. in a specific area helps them narrow down the field of potential candidates. On the other hand, from the inidividual's perspective, having a degree in a specific area might preclude consideration for jobs that are tangential to this area, even though the person is nonetheless qualified. So, my guess is that it is a blend of wanting to appear qualified for many careers in the field of science, to not wanting to appear as a "jack of all trades and master of none." The choice of how to spin one's qualifications is perhaps best left to the individual.