One reason for Mixed Economies is presented here. Another reason is presented below. First;
The definition of a mixed economy:
An economic system in which both the private enterprise and a degree of state monopoly (usually in public services, defense, infrastructure, and basic industries) coexist. All modern economies are mixed where the means of production are shared between the private and public sectors. Also called dual economy.
Laissez-Faire Capitalism is the idea that there should be no rules that in any way hinders private enterprise.
Here is the definition of Laissez-Faire Capitalism:
Laissez-faire capitalism is an economic system. Capitalism involves the ownership of property by individuals. The individual's goal is to use this property, or capital (buildings, machines, and other equipment used to produce goods and services), to create income. Individuals and companies compete with one another to earn money. This competition between companies determines the amount of goods produced and the prices company owners may demand for these goods. The French term laissez-faire literally means "to let people do as they wish." Thus, supporters of laissez-faire capitalism do not want the government to interfere in business matters, or if governments do involve themselves in business matters, to keep government influence to a minimum.
One result of no rules in private enterprise is that a person with money and thus the ability to buy influence (i.e. allot of money equals greater power, political and social) can destroy any chance of a competitor entering the marketplace. In fact, without rules and law, people tend to be greedy and selfish. Something which is normally well-known.
With no law there is no control over anyone with power using it unfairly against someone who is socially and politically weaker. Generally, this is seen as immoral by all religions and philosophies as being ruthless means there is no 'charity' and others must be manipulated to gain even more wealth and control (a never ending process).
That is why religious sources tend to be against the 'might is right' belief embedded in Laissez-Faire Capitalism.
The following is a religious explanation(from Christianity) which is naturally against the type of behavior which takes from fellow human beings to the detriment of society;
Darwin's ideas played a critically important role in the development and growth, not only of Nazism and communism, but also of the ruthless form of capitalism as best illustrated by the robber barons. While it is difficult to conclude confidently that ruthless capitalism would not have blossomed as it did if Darwin had not developed his evolution theory, it is clear that if Carnegie, Rockefeller, and others had continued to embrace the unadulterated JudeoChristian worldview of their youth and had not become Darwinists, capitalism would not have become as ruthless as it did in the late 1800s and early 1900s. Morris and Morris (p. 84) have suggested that other motivations (including greed, ambition, even a type of a missionary zeal) stimulated the fierce, unprincipled robber baron business practices long before Darwin. Darwinism, however, gave capitalism an apparent scientific rationale that allowed it to be taken to the extremes that were so evident in the early parts of last century.
The basic argument against Laissez-Faire Capitalism (as opposed to a mixed economy with laws to help keep the market fair - see definition above) is that without rules, ruthlessness and "might is right" reigns supreme. Allowing the rich and powerful to take advantage of the weak.
In the feudal system, allot of power (through control of land and resources) was given to a few people by a king. These people would then do everything they could to take whatever they could at the cost of society and every other human that could be conned (that is generally in a different clan or family, though this didn't hold in all cases).
Such economic behavior (and an effect of Laissez-Faire Capitalism) was and is referred to as "Robber Barons";
What Does Robber Barons Mean?
A disparaging term dating back to the 12th century which refers to:
1. Unscrupulous feudal lords who amassed personal fortunes by using illegal and immoral business practices, such as illegally charging tolls to passing merchant ships.
2. Modern-day businesspeople who allegedly engage in unethical business tactics and questionable stock market transactions to build large personal fortunes.
Regulating immoral business practices is an old function of modern democracies and modern economies. This is another reason why in the modern world government is mixed with private enterprise. To provide rules and a framework for a fairer society with more opportunity for all its citizens not just a few who happen to be on top and thus have the wealth and influence to get more and more while giving back less and less to the community that these individuals are from.