The Church has been through this all before. I assume people don’t know about it only because they have been so poorly catechized.
In the 3rd century, during persecutions, there were Christians who were martyrs and there were Christians who lapsed, who renounced their Christianity. After the persecutions, the Church split between those who accepted the lapsed back and those who excluded them. The exclusionists became known as Donatists, an heretical sect that was split off from the Catholic Church.
One of the things St Augustine worked out contending with them was the doctrine of ex opere operato. The sacraments are not valid because of the sanctity of the priest, but because the working of the ritual. In this doctrine is an acknowledgement that priests who are sinners are still members of the Church, still capable of performing the Church’s rituals. This affirms an inclusive Church against those who wanted strict rules excluding some people.