You can have a market economy without immortal corporations. This is something Quigley pointed out a long time ago. The varieties of persona ficta we have created is unlike anything in history. Even the old British charters were limited in terms of either duration, operations, or both. Modern corporations can do whatever they want for as long as they want. They are mostly insulated from criminal law. An individual poisons the town, he gets the lynch mob. A team of executives poisons the town (after days/weeks of cool deliberation), they get bonuses.

Most companies are not publicly traded. Getting rid of the stock market doesn't mean that your local coffee shop is now state-owned. And if they sell specialty coffee, it may not even impact the price of the beans.