of course the problem is that things are very interrelated at a company. maybe you can't hire good developers if you don't have good HR people to recruit them. if you have bad or not enough cleaning staff, maybe none of your "profit center" employees are actually willing to work for you because your office is filthy. maybe the event planning staff do really good parties that help with retention.
I guess I'm inclined to agree with you that there's no clear, workable definition of "cost center" or "profit center", but there are certainly areas of your company that generate more ROI than others, and I think that's kinda the point of this (crude) way of thinking about it.