"The power to bind and loose was given to all the Apostles, according to Holy Tradition and Scripture (John 20:22-23)" - I affirmed this already.
"The keys are the authority to bind and loose sins."-This is where you err. The keys are not this. To prove it, note that in the same Gospel according to Matthew (the only Gospel where the "keys" are mentioned Mt.(16:18-19)) two chapters later in (18:18) the power to bind and loose sins was granted to the rest of the Apostles however there is no mention of the "keys" given to the other Apostles.
"There is no other authority other than Christ Himself" - Of course Christ Himself is the ultimate Authority. No Catholics would dream of placing a man equal with God. This was a silly straw man argument. And to that sill point: you then are a hypocrite to deny authority to the Apostolic priesthood, because even you yourself acknowledge the authority of the Patriarchs belonging to the Eastern Orthodox Church.
"nor the consensus of the Church fathers indicates that bishops who succeeded Peter received any "keys", or that Peter alone had the keys"- You err again. Here are some references from the Early Church Fathers on this:
Clement of Alexandria
“[T]he blessed Peter, the chosen, the preeminent, the first among the disciples, for whom alone with himself the Savior paid the tribute [Matt. 17:27], quickly grasped and understood their meaning. And what does he say? ‘Behold, we have left all and have followed you’ [Matt. 19:27; Mark 10:28]” (Who Is the Rich Man That Is Saved? 21:3–5 [A.D. 200]).
Tertullian
“[T]he Lord said to Peter, ‘On this rock I will build my Church, I have given you the keys of the kingdom of heaven [and] whatever you shall have bound or loosed on earth will be bound or loosed in heaven’ [Matt. 16:18–19]. . . . Upon you, he says, I will build my Church; and I will give to you the keys, not to the Church” (Modesty 21:9–10 [A.D. 220]).
The Letter of Clement to James
“Be it known to you, my lord, that Simon [Peter], who, for the sake of the true faith, and the most sure foundation of his doctrine, was set apart to be the foundation of the Church, and for this end was by Jesus himself, with his truthful mouth, named Peter, the first fruits of our Lord, the first of the apostles; to whom first the Father revealed the Son; whom the Christ, with good reason, blessed” (Letter of Clement to James 2 [A.D. 221]).
Origen
“f we were to attend carefully to the Gospels, we should also find, in relation to those things which seem to be common to Peter . . . a great difference and a preeminence in the things [Jesus] said to Peter, compared with the second class [of apostles]. For it is no small difference that Peter received the keys not of one heaven but of more, and in order that whatsoever things he binds on earth may be bound not in one heaven but in them all, as compared with the many who bind on earth and loose on earth, so that these things are bound and loosed not in [all] the heavens, as in the case of Peter, but in one only; for they do not reach so high a stage with power as Peter to bind and loose in all the heavens” (Commentary on Matthew 13:31 [A.D. 248]).
Cyprian of Carthage
“The Lord says to Peter: ‘I say to you,’ he says, ‘that you are Peter, and upon this rock I will build my Church.’ . . . On him [Peter] he builds the Church, and to him he gives the command to feed the sheep [John 21:17], and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were that also which Peter was [i.e., apostles], but a primacy is given to Peter, whereby it is made clear that there is but one Church and one chair. So too, all [the apostles] are shepherds, and the flock is shown to be one, fed by all the apostles in single-minded accord. If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he [should] desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?” (The Unity of the Catholic Church 4; 1st edition [A.D. 251]).
Cyril of Jerusalem
“The Lord is loving toward men, swift to pardon but slow to punish. Let no man despair of his own salvation. Peter, the first and foremost of the apostles, denied the Lord three times before a little servant girl, but he repented and wept bitterly” (Catechetical Lectures 2:19 [A.D. 350]).
“[Simon Magus] so deceived the city of Rome that Claudius erected a statue of him. . . . While the error was extending itself, Peter and Paul arrived, a noble pair and the rulers of the Church, and they set the error aright. . . . [T]hey launched the weapon of their like-mindedness in prayer against the Magus, and struck him down to earth. It was marvelous enough, and yet no marvel at all, for Peter was there—he that carries about the keys of heaven [Matt. 16:19]” (ibid., 6:14).
“In the power of the same Holy Spirit, Peter, both the chief of the apostles and the keeper of the keys of the kingdom of heaven, in the name of Christ healed Aeneas the paralytic at Lydda, which is now called Diospolis [Acts 9:32–34]” (ibid., 17:27).
Ephraim the Syrian
“[Jesus said:] Simon, my follower, I have made you the foundation of the holy Church. I betimes called you Peter, because you will support all its buildings. You are the inspector of those who will build on Earth a Church for me. If they should wish to build what is false, you, the foundation, will condemn them. You are the head of the fountain from which my teaching flows; you are the chief of my disciples. Through you I will give drink to all peoples. Yours is that life-giving sweetness which I dispense. I have chosen you to be, as it were, the firstborn in my institution so that, as the heir, you may be executor of my treasures. I have given you the keys of my kingdom. Behold, I have given you authority over all my treasures” (Homilies 4:1 [A.D. 351]).
Pope Damasus I
“Likewise it is decreed . . . that it ought to be announced that . . . the holy Roman Church has been placed at the forefront not by the conciliar decisions of other churches, but has received the primacy by the evangelic voice of our Lord and Savior, who says: ‘You are Peter, and upon this rock I will build my Church, and the gates of hell will not prevail against it; and I will give to you the keys of the kingdom of heaven . . . ’ [Matt. 16:18–19]. The first see, therefore, is that of Peter the apostle, that of the Roman Church, which has neither stain nor blemish nor anything like it” (Decree of Damasus 3 [A.D. 382]).
Jerome
“‘But,’ you [Jovinian] will say, ‘it was on Peter that the Church was founded’ [Matt. 16:18]. Well . . . one among the twelve is chosen to be their head in order to remove any occasion for division” (Against Jovinian 1:26 [A.D. 393]).
Pope Innocent I
“In seeking the things of God . . . you have acknowledged that judgment is to be referred to us [the pope], and have shown that you know that is owed to the Apostolic See [Rome], if all of us placed in this position are to desire to follow the apostle himself [Peter] from whom the episcopate itself and the total authority of this name have emerged” (Letters 29:1 [A.D. 408]).
Council of Ephesus
“Philip, presbyter and legate of [Pope Celestine I] said: ‘We offer our thanks to the holy and venerable synod, that when the writings of our holy and blessed pope had been read to you . . . you joined yourselves to the holy head also by your holy acclamations. For your blessedness is not ignorant that the head of the whole faith, the head of the apostles, is blessed Peter the apostle’” (Acts of the Council, session 2 [A.D. 431]).
“Philip, the presbyter and legate of the Apostolic See [Rome] said: ‘There is no doubt, and in fact it has been known in all ages, that the holy and most blessed Peter, prince and head of the apostles, pillar of the faith, and foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Savior and Redeemer of the human race, and that to him was given the power of loosing and binding sins: who down even to today and forever both lives and judges in his successors’” (ibid., session 3).
Now, moving on to my final point:
Maybe you just skimmed over my response to the mormon but here I will quote myself again so you can read it and see that I affirmed everything you said here. The only thing you disagree with is the symbol of authority that was given to St.Peter uniquely because the successors to the Apostles in the Eastern Orthodox Churches later went in schism with Rome... But here was my initial post that you responded to:
The keys were given only to St.Peter.
Not to anyone else. The power of binding and loosing sins was later given to the rest of the Apostles but the keys alone went to St.Peter and nobody else...
And the answer to your question is yes. Yes, the Catholic Church has the metaphoric keys because St.Peter himself received them, and his successor received them from him, then his successor received them, on and on, the successors to the Episcopal seat at Rome all received these keys... Only the humble can believe it...