Well, there are several competing organizations, but as the scale and visibility effects of mass media businesses make one or two of them very large and the others very niche.
In any case, a “free market” arbitration system won’t be necessarily “more just” to the fans of the sport. It might be, but that’s not a foregone conclusion.
It all boils down to the structure of incentives that the judges are responding to.
The federation judges may be responding to reputation and perhaps bribes and influence trafficking, whereas the free market judges might be responding to whatever they perceive to be the interest of their clients.
You can think of the UFC fans as their ultimate clients, and that’s not wrong in a broad sense, but that’s also very naive.
Their clients are the people directly taking the decisions about hiring them, so you have at least a few layers of decisions buffering them from the UFC fans.
And they will be more responsive to these middle man (UFC organizers, agents and impresarios) than to UFC fans.
Therefore, it’s not clear that they will resolve fights in a fashion that is considered, by UFC fans, as fairer.
It will depend on whether these middle man running the show consider profitable to increase fairness or not.
UFC fans respond to fairness to a certain point, but they are not zealots, and that’s evident once we consider that some of the greatest fanbases in the sport were amassed by notorious juicers, cheaters and overal treacherous scumbags, like Chael Sonnen.