> The state is the only authorized monopoly of violence and they should treat unproven and untrue as identical, and the only place where that decision is made is in a courtroom.

This is completely wrong. If the state treated all accusations as untrue prior to conviction, they would not send armed men to haul you to prison, bar you from release unless you can bail yourself out (or sometimes not at all), and not have a prosecutor charge you with a crime.

This is no petty distinction. In order to function in its judiciary role, the state in fact must distinguish between plausibly true accusations and not plausible accusations, and must treat certain plausibly true accusations as "unproven" but not untrue, and take steps to make sure the accused does not flee into another country or commit further crimes.