No. The high priest's role was to confess the nation's sins on the day of atonement. Every other day it was every person's responsibility to confess their own sins and offer their own sacrifice. That is why we are admonished in Hebrews to confidently approach the throne of grace ourselves. The sacrifice has been offered; it merely awaits our confession.
The law is only a shadow of the good things that are coming–not the realities themselves. For this reason it can never, by the same sacrifices repeated endlessly year after year, make perfect those who draw near to worship. If it could, would they not have stopped being offered? For the worshipers would have been cleansed once for all, and would no longer have felt guilty for their sins. But those sacrifices are an annual reminder of sins, because it is impossible for the blood of bulls and goats to take away sins.
Sin confession is like the blood of bulls and goats, a reminder of sins. It doesn't set us free like Jesus' blood which stops the offerings. Sin confession is practically identical in concept to the old sacrifices, that had to be done again and again. Unlike believing in Jesus who took all our sins once and for all, and in Him we have total forgiveness.