> This requires that we accept that there is such a thing as a neutral procedure...

Yes, it does. And we live in a society. So by extension we do already accept that neutral procedures are possible and that we have achieved them.

The English Common Law systems and their derivatives are an astonishing success in achieving general fairness. People arguing against it have, with remarkable consistency, failed to come up with anything that reaches it's level of neutrality. In fact, normally people struggled to come up with general criticism beyond accusations that specific individuals didn't follow the procedures properly or relatively minor tweaks to the administrative details.

Neutral procedures are a solved problem, the tricky part is convincing the law enforcement system to do things by the book.