I believe the exact opposite: you need collusion with the state to establish a monopoly. And you don’t have a pure free market as long as there is a state that puts its heavy hand on the scale to favour one group over another.

The free market has its flaws, but many blame it for the ills caused by corruption and lobbying of politicians.

There has never been a truly free market anywhere in the world, let alone ‘pure’, so I don’t see why you use this adjective at all.