The question is, what happens with the next generation? Also, there are public companies that are family-controlled, such as Ford, through two classes of stock. Family control of large companies is more common outside the US, in countries which allow cross-holding and have weak shareholder rights. Samsung and Hyundai are family-controlled, but the family owns under 1% of the stock. A successful company that tried that in the US would face a hostile takeover.
Arguably, Google and Facebook are "family-controlled", with two classes of stock that keep the founders in control.