2TI.2:2 does not say “infallible people” are needed to carry it out, but only “faithful people” who (v.15) “study to show themselves approved unto God…rightly dividing the word of truth”.
In 2 Tim 3:16-17 we read, “All scripture is inspired by God and profitable for teaching, for reproof, for correction, and for training in righteousness, that the man of God may be complete, equipped for every good work.”
So, the Scriptures are a tool for “teaching, for reproof, for correction, and for training in righteousness,” but who is to use this tool for these purposes? That is, who has the authority to teach, reproof, correct, and train others in righteousness? The “man of God” has this authority. But, who is the “man of God?”
The “man of God” is
not “anyone with a Bible and the ability to read it.” A short survey of Scripture’s use of the title will reveal that this is a privileged title that cannot be simply taken upon oneself:
Moses - “This is the blessing with which Moses the man of God blessed the children of Israel before his death.” (Deut. 33:1)
“Then the people of Judah came to Joshua at Gilgal; and Caleb the son of Jephunneh the Kenizzite said to him, ‘You know what the LORD said to Moses the man of God in Kadesh-barnea concerning you and me.’” (Josh. 14:6)
The Angel of the Lord - “Then the woman came and told her husband, ‘A man of God came to me, and his countenance was like the countenance of the angel of God, very terrible; I did not ask him whence he was, and he did not tell me his name…’ Then Manoah entreated the LORD, and said, ‘O, LORD, I pray thee, let the man of God whom thou didst send come again to us, and teach us what we are to do with the boy that will be born.’” (Jud. 13:6, 8)
Samuel - “The servant answered Saul again, ‘Here, I have with me the fourth part of a shekel of silver, and I will give it to the man of God, to tell us our way.’” (1 Sam. 9:8)
Elijah - “And she said to Elijah, ‘What have you against me, O man of God? You have come to me to bring my sin to remembrance, and to cause the death of my son!’” (1 Kings 17:18)
Elisha - “And she went up and laid him on the bed of the man of God, and shut the door upon him, and went out… When Elisha came into the house, he saw the child lying dead on his bed.” (2 Kings 4:21, 32)
David - “According to the ordinance of David his father, he appointed the divisions of the priests for their service, and the Levites for their offices of praise and ministry before the priests as the duty of each day required, and the gatekeepers in their divisions for the several gates; for so David the man of God had commanded.” (2 Chr. 8:14)
St. Timothy - “But as for you, man of God, shun all this; aim at righteousness, godliness, faith, love, steadfastness, gentleness.” (1 Tim. 6:11)
Contrary to the opinion that the “man of God” can be any Christian without distinction, Scripture itself will not allow such an interpretation, insisting that the “man of God” is a figure of authority, either commissioned by God directly through Divine Intervention (such as Moses or the Angel), or appointed by another holder of authority (such as Samuel, David, Elisha, and St. Timothy).
you have to know by now what I’m going to ask for. I also know what you’re gonna give me and you also know what I’m going to say about it and I also know how you will refute what I say. Fun times! 
I’ll speak for myself, thank you. I say both the mustard plant, and the mustard seed. Who am I to refuse any gift God has given me… be it His Church, Sacred Tradition, or Sacred Scripture. If you want to pick and choose which of God’s gifts you accept & reject,t that’s on you. Speaking for myself, I will accept all that the Lord has given. 
The question asserts that God transferred authority from one entity to another. Thus, the argument fits the question. If Jesus had to transfer authority to a different Church or a different group of people then the original church would necessarily have failed, no?