A: To answer the question we need to differentiate between priesthood authority, priesthood keys, and priesthood power.
We know that the original church was organized with a chief apostles Peter at the head of 12 apostles (Eph. 4: 11). The church also had 7 evangelists or presidents and had seventy elders. On the local level we have individual bishops (episcopate) who had authority over elders (presbyter) and deacons (deaconos). We also get a clue from the Bible that Elders were authorized to do things deacons didn't do. When the Bible says who can bless and annoint, it says call upon the elders (James 5: 14).
Clement criticizes those in Corinth who removed their Bishop, and said Bishops were to be appointed by eminent men in the hierarchy and not voted in by the congregation. And then the appointment, Clement said, was to be presented before the church for a vote of consent and sustaining (1 Clem 41:1, 42:5, 44:1-5).
Ignacius tells the church to do nothing without the Bishop including baptisms, lords supper etc. So if there is a priesthood of all believers, there still is the issue of keys (Epistle of Ignatius to Hero: 3,Epistle of Ignatius to the Smyrnaeans: 8). You should remember that while the sealing authority was given to all the Apostles In Matt 18, only Peter was given Keys (Matt 16:18-19).
Okay, so what's the difference:
Priesthood authority is the authority to act in the name of God and perform an ordinance, sacrament, covenant marriage, Lords Supper that is valid in heaven in the eyes of God.
Priesthood keys are not just the authority to administer an ordinance, but it is the the authority to authorize that a baptism, Lords Supper, or covenant marriage can be done. A person may have the authority to administer the ordinance, but keys are necessary to authorize that the ordinance be done. The concept of keys is genius because it prevents a person from receiving priesthood authority and then splitting off and thinking he can form his own authorized church. All authority is derived from the same keys. And only Peter and all the Apostles together held all the keys.
Even with priesthood keys and authority, there still is the issue of power. Just because someone has authority, a person must empower that authority. This empowerment of priesthood authority is based on the atonement of Jesus Christ, repentance, and personal righteousness. And the power of the Priesthood is the Holy Ghost and the Holy Ghost does not dwell in unholy temples (1 Cor. 3: 16). This is why the Apostles were unable to cast out devils on one occasion and Christ told them these did not come out but by prayer and fasting. There wasn't a problem with authority but empowerment (Matt. 17: 21).
So, after the death of the Apostles and many of the Early Church Fathers and Bishops, the keys of the Priesthood, which are passed down in succession by the laying on of hands (1 Tim. 4: 14), was lost to the Earth. While individual Bishops are given some keys to preside over a local congregation only the Chief Apostles, and the Twelve Apostles as a group hold and exercise all Priesthood keys. Another important aspect of the kingdom of God is its hierarchy. The Bible and the Early Church Fathers made it abundantly clear that church leadership was supposed to be appointed from the top down and not elected from the bottom up. Voting does not represent and does not always reflect the mind and will of God.