The danger of calling companies owned by individuals or group of people "Private Companies"

How can Companies that are open to the public, serve the People of a Nation and supposed to be subjected to national laws be called Private Companies? They are Public Companies owned and run by individuals or group of people "once they are opened to the Public." No need to be called "Private" anymore as they are now serving the Public & have to be transparent/accountable to them. What do they need to be private for when they serve thousands/millions of people? What are they hiding? They should be subjected to all good/reasonable laws of Nations they serve . All rules made by such companies should be in harmony with the basic national laws and principles. This won't stop them from running very effectively and profitably.

If you allow such companies to be run privately(instead of openly/publicly) you could be indirectly excluding them from just laws that could make them to be very transparent, accountable to the public/law, etc .. Imagine an evil, non-transparent and non-accountable company growing too large and powerful in a country that values transparency and accountability. That is dangerous.