Markets always exists as long as people want to exchange one thing for another, by definition.

Concepts such as person or property are required premises for such a market system to happen, be it by formal laws or tacit consensual behaviors.

Yes, and throughout human history, there has always been the concept of owned property.

Yes and you're allowed to regulate markets into things that actively benefit society and not just sucking blood from people willy nilly.

No one said you couldn't.

We are allowed as in, no formal rule forbid it is one thing. But if all the rules favors oligarchic accumulation with reinforcing loop, it's unlikely that the resulting dynamics will fall into a loophole of equal redistribution of wealth where social harmony thrive.