Corporations also can't do what they want - for instance they cannot commit fraud, evade taxes, sell dangerous products and so on.
You have something like that in sports, when in order for participants to compete freely, they are being tested for illegal drugs, so that no one has a unfair competitive advantage.
Free != do what you want.
> an economic system in which prices are determined by unrestricted competition between privately owned businesses.
"Unrestricted competition", to me, clearly says that businesses should be able to compete without such restrictions as being split up by the government if they become too big.
Or this definition from investopedia (the first actual result on Google):
> The free market is an economic system based on supply and demand with little or no government control.
The government splitting up businesses is certainly a form of government control.
However, Wikipedia's first paragraph is:
> In economics, a free market is a system in which the prices for goods and services are self-regulated by buyers and sellers negotiating in an open market without market coercions. In a free market, the laws and forces of supply and demand are free from any intervention by a government or other authority other than those interventions which are made to prohibit market coercions. Examples of such prohibited market coercions include: economic privilege, monopolies, and artificial scarcities.
Apparently, the government imposing control and restricting competition is part of Wikipedia's definition of a "free market", so extremely harsh anti-monopoly and laws against anti-competitive behavior fits perfectly well in Wikipedia's definition, but makes the market less free according to the definitions I've been following.
The important part is, I agree that a lot of government intervention is required to make markets function efficiently. I just personally wouldn't call that a "free market", rather a well-regulated market.
It would certainly have the potential to make the market work better and improve competition, but that's not what a free market is.