Anybody~What do the ante-nicene fathers say about this? Seems like they'd have had to deal with this issue when they decided to accept or reject the successors to the original apostles.
I still don't see anything that implicitly makes the point that Jesus has to do the appointing. Here is a qoute (Matt. 16:18) and some commentary on it from the Douay-Rheims bible. Note that Peter was given the authority to do things, such as appoint apostles, when he was given the keys of the kingdom. This commentary makes sense to me.
"18 And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it. Thou art Peter, etc... As St. Peter, by divine revelation, here made a solemn profession of his faith of the divinity of Christ; so in recompense of this faith and profession, our Lord here declares to him the dignity to which he is pleased to raise him: viz., that he to whom he had already given the name of Peter, signifying a rock, John 1:42, should be a rock indeed, of invincible strength, for the support of the building of the church; in which building he should be, next to Christ himself, the chief foundation stone, in quality of chief pastor, ruler, and governor; and should have accordingly all fulness of ecclesiastical power, signified by the keys of the kingdom of heaven. Upon this rock, etc... The words of Christ to Peter, spoken in the vulgar language of the Jews which our Lord made use of, were the same as if he had said in English, Thou art a Rock, and upon this rock I will build my church. So that, by the plain course of the words, Peter is here declared to be the rock, upon which the church was to be built: Christ himself being both the principal foundation and founder of the same. Where also note, that Christ, by building his house, that is, his church, upon a rock, has thereby secured it against all storms and floods, like the wise builder, Matthew 7:24-25. The gates of hell, etc... That is, the powers of darkness, and whatever Satan can do, either by himself, or his agents. For as the church is here likened to a house, or fortress, built on a rock; so the adverse powers are likened to a contrary house or fortress, the gates of which, that is, the whole strength, and all the efforts it can make, will never be able to prevail over the city or church of Christ. By this promise we are fully assured, that neither idolatry, heresy, nor any pernicious error whatsoever shall at any time prevail over the church of Christ.