It is impossible to know the answer to this question with absolute certainty. However, we can speculate that this system has come to dominate because it offers a balance between the potential for economic growth and consumer goods on the one hand and the guarantee of stability and safety from economic harm on the other.
It is logical that people come to like free market economies. These economies offer people the opportunity to have a better life. They offer the opportunity to get richer. They tend to cause a lot of consumer goods to be produced that improve people’s quality of life. This makes these systems attractive.
However, people also want to feel that they are economically secure. This is the attraction of a system in which the government is more involved. People like to feel that someone will help them if they lose their jobs. They like to feel that they will be guaranteed a pension when they retire. They like to feel that they will be protected from companies that want to take advantage of them.
People do not tend to want a pure market system (because it is too dangerous) or a pure command economy (because it is too restrictive). They try to have the best of both worlds, and that is why the modified free enterprise system has come to dominate.