Ever thought about what is the #1 problem all countries face? I searched and multiple sources said that an economy's number one problem is scarcity. There is an unlimited demand from humans but there are only limited resources. It becomes now a problem when the government has to answer these questions:
1. What to produce?
2. How to produce?
3. Whom to distribute the product?
Governments doesn't really need to answer these questions since there are entrepreneurs who would sharply identify the needs of people around and turn it into a business activity.
This is why the private sector is very important to coexist with the government so they can provide supplies of direct consumers need and make a living from satisfying clients and revenue for the government.
On the other hand the government is needed to regulate their activities so their actions are properly guided in the interest of the public they serve.