If it turns out there really is no free will. What will happen? Do we get a kind Utopia? Or fascism where you are mistreated based on your lot in life?
There's no functional difference, unless you can accurately predict someone's actions, and to do that you'd need to predict the environment in which someone is making choices as well, which requires omniscience. So, there's no functional difference.
But we know for sure that the universe is not deterministic.
From a fundamental level, it is probabilistic.
Simple experiments can show this chaotic action.
Take for example the dripping tap experiment. The time for next drop cannot be predicted by knowing the timing of the previous drops!
This is not a random process, there is a pattern, but it is also clearly not deterministic.
The uncertainty principle says what the limits are on our knowledge of a given scenario, not that the universe which is running the show has such a limit.
I'm saying 'we'- humans, don't enter in to it at all. Knowledge and prediction are human things. I'm saying they don't apply to the universe itself which is what is running things. The state of things is what it is, irrespective of ourselves. We humans will never know enough to be able to predict perfectly, but that doesn't mean the matter and nature aren't running deterministicly.
Remember the reasons we have punishments? To discourage further misdeeds. Also, to restore justice by inflicting suffering on those who deserve it. Punishments would still be dished out for pragmatic reasons, but retributive punishment would be rendered entirely meaningless.
It would also shatter all sense of acomplishment an individual could have. All that would be left is maybe a perverse pride in knowing you where born "better" than others.
I don't think society would survive if it was a common knowledge.
Like I said, how can you prove that free will exists now? We could very well already live in your scenario, and the world isn't ending because of a lack of free will (if it doesn't exist). I mean, it is ending, but not because of free will or the lack thereof.