Yes you can do a million tests but the biases and failures of the neural net are chosen by human developers, a miniscule subset of citizens who themselves have some form of bias depending on their educational background, places where they grew up, family and friends etc. While you can replace a human in a powerful position with another one, since we do not know how to surgically correct individual weights in order to remove a specific decisional bias from a neural net, we can only retrain it and hope for the best. Because we are humans ourselves, we can understand the incentives of other humans and create adequate mechanisms to correct for their selfishness and their bias but what would be the incentive of an all powerful neural net? Which loss is it minimizing? And how does it know the citizens' preferences in the present and in the future? If the citizens stop feeding it (accurate) information at one point in time, will it still be the benevolent dictator that it was supposed to be?

*Edit: Another counterargument that generally applies to neural nets making decisions for human activities is the argument of accountability. While you can put on trial a bad politician for their harmful-to-society decision making, who is to blame when the neural net will inevitably spew the wrong output on an issue that it has not encountered before and a policy decision will be made based on that? Will we put the developers on trial?