Isn't one of the central claims of this theory that the Apostles directly appointed Bishops?
the appointment doesn't matter. The consecration is what matters for apostolic succession.
Right now, the communist government of China is trying to appoint "Catholic" bishops. They are not real bishops (or even real Catholics). Just because they are appointed bishop by the government of China doesn't mean anything. They would only be real bishops if they were consecrated by a bishop acting in good faith with the Church.
hope that helps
It's not just a theory - it's the truth. There is historical evidence to back it up. Here is an example:
Clement's Letter to the Corinthians 42:4–5, 44:1–3 (A.D. 80):
"Through countryside and city [the apostles] preached, and they appointed their earliest converts, testing them by the Spirit, to be the bishops and deacons of future believers. Nor was this a novelty, for bishops and deacons had been written about a long time earlier. . . . Our apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry."
Clement was St. Paul's friend, and is mentioned in Philippians 4:3: “And I intreat thee also, true yokefellow, help those women which laboured with me in the gospel, with CLEMENT also, and with other my fellowlabourers, whose names are in the book of life.”
Who else would have? James, an apostle, led the church of Jerusalem until his death when Symeon succeeded him. Certainly St Paul left someone in charge of the churches he founded when leaving to preach elsewhere, and St Paul also tells of the requirements for Bishops.