I never claimed the Gp made any assumption to begin with. Beyond any reasonable doubt means precisely that. It can vary from person to person and from group to group. The state is indeed very powerful compared to the individual. But the mighty hammer you speak of simply implies that the state can bring more resources to bear when prosecuting. This only means in principle that the state can drag a trial longer (and from which we are protected by the right to a speedy trial) or that they can expend more effort gathering evidence against an accused.

Your argument about individual members of society however is, with respect, flawed. The masses of society, when all working towards a common goal are not tiny droplets in the pond but indeed the mighty torrent that can sweep away even so powerful an entity as the state. To advocate for a lower standard of evidence based on the fact that "everyone knows he is guilty" is, as mentioned, to advocate for a trial system based on mob mentality. Furthermore, public opinion can can be easily swayed by what is reported to it and I will spare this thread the question of the media or powerful individuals like Trump or Russia or Clinton etc using the media to subvert public opinion.

The system again may not be perfect but it is there to protect not only from the might of the state but also from the dictatorship of the masses which may, unlike the court system, have their own reasons for convicting someone, reasons which may not even have anything to do with the actual matter. This is even more problematic as the court system is at least subject to review and appeal whereas the masses have absolutely no check on them.