I think the assumption that jurors are invariably reasonable, as opposed to on average reasonable is a pretty heroic assumption not well supported by the history of trial by jury though.
Estimates of wrongful conviction are between .13%-5% (wikipedia, miscarriage of justice), however the main thing that trial by jury affords is transparency and perception of fairness, since you are convicted by your peers and not some politician with questionable incentives.
Further, the prosecutor has real power that far outweighs the power of the accused. Juries imperfectly provide an offset to that power imbalance.