The whole concept of non-family-run corporations is barely 200 years old. At that point in time, it literally took an act of the legislature to form a corporation, and this right was typically only granted for a limited time for a very specific purpose (i.e. specifically and only to build a railroad between two specific cities, and set to come up for renewal in a few years).
On the contrary, the NYSE was founded in 1792. State Street Bank and Chubb Insurance Group were both founded before 1800, and are not family-owned AFAICT.