There are precedents for leadership succession in the Old Testament.
An example:
"Now Joshua son of Nun was filled with the spirit of wisdom because Moses had laid his hands on him. So the Israelites listened to him and did what the Lord had commanded Moses". Deut. 34:9
Jesus refers to the "chair of Moses" (a precedent for the chair of Peter) in Matthew 23.
"Then Jesus spoke to the multitudes and to his disciples, saying: The scribes and the Pharisees have sitten on the chair of Moses. All things therefore whatsoever they shall say to you, observe and do: but according to their works do ye not." Matthew 23:1-3
Jesus is the cornerstone; the apostles (led by Peter) were the foundations.
"Built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief cornerstone..." Eph. 2:20
And the wall of the city had twelve foundations: and in them the twelve apostles of the Lamb. Rev. 21:14
"And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it. I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven. Matthew 16:18-19
The keys were given to Peter, not Paul. Stewardship is passed to each successor of Peter in his turn.
This only makes my point that there ONLY twelve apostles. There is nothing to say keys were not given to the other eleven apostles. It only makes sense if each of them represents a wall and each had a gate which would require a key. Our jury of twelve will each have a hand in the binding in Heaven and earth. There is no room for for succession in this instance. In Joshuas' case someone had to finish the journey that Moses had started. Moses, as you recall, was not allowed to enter the Promised Land.