I don't have any problem with a market economy, per se, but I do have a BIG problem with capitalism.
In my preferred version of state socialism, there is no accumulation of capital, and thus no capitalism. All large industries and large-scale services are socialized, owned by the people and managed by the state (or by worker cooperatives, where practical).
In my version of a market economy, people can own and run small companies, hire employees, set prices, make a profit... that's all fine. But they can't buy their competitors and either take them over or put them out of business. They can't open franchises, where they sell (or rent) the right to operate a different company with the same name. They're not allowed to buy their suppliers and create a conglomerate. They aren't permitted to grow so large that the market no longer operates fairly. And every business owner's wealth will be capped with a highly progressive tax structure (which is the price of using the commons to turn a profit).
So, the marketplace as such is not the problem. The problem is capitalism.
@breadandcircuses I always capture this apparent contradiction by leaning on the phrase "Capitalism isn't 'free markets': Capitalism means that high-rolling investors make the laws."