We don't need theoretical market socialism; we had actual existing Yugoslavia.
Although it functioned better than centrally planned socialism, it still had lots of issues related to prices, particularly of capital. Who provides capital for enterprise? In practice, the state. And this ran into the same political economy issues with centrally planned economies. What happens when a company is about to go under? Unemployment is bad, so the worker-owned company gets a bail out. Who can start a firm? Well, better make sure your company satisfies the objectives of your local government.
You could theoretically have market socialism, where the only difference from market capitalism would be the lack of distinction between workers and owners. Gig economy would be its kryptonite, though: if allow it you are back to exploiting workers, if you ban it you will also ban a whole lot of actual self-employed professionals.