"So why is there need for any intercessory priesthood between God and His children?"
One of the greatest of the Fathers, +John Chrysostomos wrote:
"He who honors the priest, will honor God also; and he who has learned to despise the priest, will in process of time insult God. 'He who receives you,' He says, 'receives Me' (Matt. 10:40). 'Hold your priests in honor' (Ecclus. 7:31), He says. For when a man is piously disposed towards the priest, he is much more so towards God. And even if the priest is wicked, God seeing that you respect him, though unworthy of honor, through reverence to Him, will Himself reward you. For if 'he who receives a prophet in the name of a prophet shall receive a prophet's reward' (Matt. 10:41), then he who honors and submits and gives way to the priest will certainly be rewarded. Do you know what the priest is? He is an angel of the Lord. If you despise him, you despise not him, but God who ordained him.
But how does it appear, you ask, that he is ordained of God? If God works nothing through his means, you have neither laver, nor are a partaker of the Mysteries, nor of the benefits of blessings; you are therefore not a Christian. What then, you say, does God ordain all, even the unworthy? God indeed does not ordain all, but He works through all, though they be themselves unworthy, so the people may be saved. For if He spoke, for the sake of the people, by an ass, and by Balaam, a most wicked man (Num. 22,23,31), much more will He speak by the mouth of the priest. What indeed will not God do or say for our salvation? By whom does He not act? For if He wrought through Judas and those others who 'prophesied' ... will He not much more work through the priests?
If we may not judge our brother, much less our teacher, let each attend to his own department. For if he teaches perverted doctrine, though he be an angel, do not obey him; but if he teaches the truth, take heed not to his life, but to his words. You are a sheep, do not be curious concerning the shepherd, lest you have to give account of your accusations against him. It is not he who speaks to you. It is Christ who thus admonishes you. But you say, 'He ought to be better than I.' Why? 'Because he is a priest'. If he is not better, ought you therefore to destroy yourself? These are the words of arrogance. Hear what Christ says, 'Every idle word that men shall speak, they shall give account thereof in the day of judgment' (Matt. 12:36).
Let us reverence that day on which he enlightened us. He who has a father, whatever faults he has, conceals them all. For it is said, 'Do not glory in the dishonor of your father, for your father's dishonor is no glory to you. And if his understanding fails, have patience with him' (Ecclus. 3:10-12). And if this is said of our natural fathers, much more of our spiritual fathers. Approach him with pious respect. Do not say he is wicked. What of that? Does one who is wicked of himself bestow great benefits on you? By no means. Everything works according to your faith. The priest performs a symbol. The Offering is the same, whether a common man, or Paul or Peter offer it. It is the same which Christ gave to His disciples, and which the priests now minister. This is in no way inferior to that, because it is not men who sanctify even this, but the Same who sanctified the one also sanctifies the other. So the world is of one faith. The Spirit immediately fell upon Cornelius, because he had fulfilled his part, and contributed his faith." Homily II on II Timothy I
St. John is a "later" source, so perhaps this from the First Epistle Of Clement To The Corinthians, Chap. XLI will explain why we believe in the necessity of a priesthood and, even more importantly the Apostolic Succession and the ancient Christian nature of this belief:
"The apostles have preached the Gospel to us from the Lord Jesus Christ; Jesus Christ has done so from God. Christ therefore was sent forth by God, and the apostles by Christ. Both these appointments, then, were made in an orderly way, according to the will of God. Having therefore received their orders, and being fully assured by the resurrection of our Lord Jesus Christ, and established in the word of God, with full assurance of the Holy Ghost, they went forth proclaiming that the kingdom of God was at hand. And thus preaching through countries and cities, they appointed the first-fruits [of their labors], having first proved them by the Spirit, to be bishops and deacons of those who should afterwards believe. Nor was this any new thing, since indeed many ages before it was written concerning bishops and deacons. For thus saith the Scripture a certain place, "I will appoint their bishops in righteousness, and their deacons in faith."
The Golden Mouth indeed!
"Peter wrote: "you are A CHOSEN RACE, A royal PRIESTHOOD, A HOLY NATION, A PEOPLE FOR God's OWN POSSESSION, so that you may proclaim the excellencies of Him who has called you out of darkness into His marvelous light;
10 for you once were NOT A PEOPLE, but now you are THE PEOPLE OF GOD; you had NOT RECEIVED MERCY, but now you have RECEIVED MERCY." (I Peter 2:9-10)"
So, I ask again, in light of the above why is there any need for intercessory priests? Paul wrote: "For there is one God, and one mediator also between God and men, the man Christ Jesus, who gave Himself as a ransom for all, the testimony given at the proper time." I Timothy 2:5-6 so to interpose any other is to diminish His role. I would take the words of Peter and Paul over the words of John Chrysostom. They had a temporally closer relationship with the Messiah. I neither honor the priest nor am I despising him. I AM HIM according to Peter.