The market isn’t free so much as it is anarchistic, according to Marx. That is, production isn’t directed by human need, which is, i think, what you refer to as communism, but by profitability. Stuff doesn’t get made based on whether people need it, it isnt made available to buy so that its available for people who need it, its all based on whether companies can make money.

The USA government does direct production somewhat, but directs it in a way that resources and the means of production (which means “the stuff that is used to make other stuff”) goes to the capitalists, individual and corporate, rather than belonging to the people. For example, in the State of Michigan, Nestle pays about $200 per year to extract millions of gallons of water from lake Michigan, meanwhile many people in surrounding areas dont have access to clean fresh water at all. While Flint is, a decade later, replacing lead lines, and government regulation now requires reporting maps of lead lines in municipalities, Chicago conspicuously is exempt, and around 400,000 households are being supplied leads contaminated water.

Another is railroads. Back in the day the government gave land to build them to the rail companies, and used the military to clear and protect the lands so that the rail companies could run them profitably. By the 70’s, passenger and commercial railroads were no longer profitable, and rail companies started going bankrupt, starting with Penn Central, and then cascading to other industries. but they were critical national infrastructure, so the US government first injected subsidies into the businesses (very similar to the “too big to fail” attitude of the 2008 great recession) and then the US Government took over the failed railroads, which created Amtrak for passenger and Conrail for commercial. In 1987, Conrail was sold off to Norfolk Southern and CSX, once the government had fixed up the failing, disintegrating infrastructure, for 1.8 B. A decent return to the taxpayers, but last year CSX generated 3.25 B in profit. Norfolk Southern reported 4.4 billion in income, but paid out a lot in “derailment stabilization” which, despite its mention in financial reports, people are still sick and reporting bad water in East Palestine OH. Also talk to someone who works for a major railroad and you’ll hear about worsening safety conditions due to deregulation. So the company is free to make money, but the people are not free to live in peace, and to raise our children in good health. These trends have been realized in other places, such as New Zealand and UK.

Depending on how you look at it, and this is how I look at it, the market isn’t free because it is controlled by the capitalists. We are allowed to use it in limited ways, like we can sell our labor on it, but when it comes to producing and selling commodities, there are often fees, restrictions, monopolizing factors that prevent people from converting our own work into a good living. In the USA, the government ensures high returns on capital investments for the capitalists. In China the system is at least somewhat blended and contradictory. Imo its very difficult to pin down exactly what the Chinese system actually is. State Capitalist doesn’t really fit, social democracy doesn’t really fit, full communist doesn’t really fit. But in the USA, the “free market” invokes Marx in “On the Question of Free Trade”:

Do not be deluded by the abstract word Freedom. Whose freedom? Not the freedom of one individual in relation to another, but freedom of Capital to crush the worker.

China has billionaires and private property. Is that not capitalist enough?