Does the graphics department at your company turn a profit? The university is a massive global business that happens to be not taxable. It doesn't mean you shouldn't run that massive global business without top-notch business acumen which I'm guessing may not be readily available in academia.
A senior professor does not just wake up one day and become a university president. If university is a business, then the professor who is to become president would have several years of "business" experience-- as university vice president, provost, dean of an academic department, etc. A professor that lacks that administrative experience does not become university president.
Many things may be seen as businesses. Accounting firms and law firms, for example. Even religion. Does not mean that Bill Gates would make a good pope. An Accounting firm does not hire someone as CEO because he has decades of experience running a software firm. The head of that Accounting firm would typically be someone who has experience in some facet of Accounting.
Not sure why the head of an academic institution be any different. The best candidates would be those that come from an academic background, but who also have considerable experience in administrative positions in academia.