Read the book Insignia and Vortex by S.J. Kincaid. You'll understand my point instantly without explanation. It's WWIII, and it's between mega monopolies that run the world and battle for the universe. The position the author writes in is against it, and the subliminal messages about prove points that are very important to this topic.
There is a reason that in the 1800s and early 1900s we organized trade unions and government arms like the FDA. When left to themselves with no regulations, corporations run rampant with corruption- at the expense of their employees (their health, safety, and a living wage particularly) and the health and safety of the consumer. Because THAT is what makes them the greatest percentage of profits.
Governments are supposedly there to serve on our behalf in the western world to work for your interests. Companies are in it for profit only. They survive and die based on income so they are only in it for the money. You might think they care for the customer but they actually care more about what's in the customers wallet. They are tied down by strict government red tape and regulations so they can't exploit people.
Left completely be itself greed and monopoly will grow to absurd levels. Companies will eat each other up until there is only the big ones left to hold a monopoly. They will stranglehold the market using normally government induced illegal and shady methods as they will grow too powerful to be challenged.
There will only be major players in the business holding their business to ransom to the people. With no regulation they can refuse you service for absolutely any reason eg food, gas, water, electricity. These companies will skyrocket their prices just because they can and there is no competition. They will rip off customers with dodgy goods and not be obligated to refund them because of no government intervention. They can lie, slander, and hide because they would be allowed to.
It would be a terrible place.
If everything was run by free-market corporations, corruption levels would range from being approximately equivalent to what they are now to being grossly higher. The government aims to protect the public interest. Its motivator is supposed to be the common good. Any corporation does not have that aim. The job of a corporation is to make a profit, not provide for the public good. History showed what happens when free markets ran everything with the Gilded Age - rampant corruption, trusts and monopolies, etc.
Free market corporations will capitalize and run by their own rules. The government has actual laws against monopolization but without those laws and regulations companies would be free to own large percentages of markets such as coal or telecommunications, food and apparel. I agree that corruption needs to be reduced but free market is not the way to do it.
Corporations, like gas companies and stores, are there to provide services for the people. Sure, of course you have two types of bad runners and all -- the imperialist beneficiary and the incompetent manager (McDonald's, MTA) lol. But other than that corporations can do so MUCH good as well. Government intervention ain't good.
A corporation is at the mercy of consumers. If consumers decide that a corporation is corrupt or unfair they can choose not to give them money. If they choose not to give the government money, they go to jail. The free market is less corrupt because it is only as corrupt as consumers.
There is no such thing as free-market corporations controlling that would be called corporatism, however I believe you question is about a free market. So If you asking about a free-market it should at least be a improvement from special interest groups controlling the parties which intern control government actions.