I've been wondering lately whether the "apostolic succession" would be better viewed as passing through the rite of baptism — and thus to all baptized Christians — instead of through the rite of consecration as a bishop.
In giving the Great Commission after the Resurrection, Jesus directed the eleven remaining disciples only to make additional disciples of all nations, baptizing them and teaching them to obey everything he had commanded (Matt. 28.19-20).
Jesus said little or nothing about how the disciples — old or new — should govern themselves; before his death, he had said only that they must serve one another. 
Neither did Jesus direct the Eleven to anoint themselves and their self-chosen successors as rulers over all other disciples; that seems to have been a later 'innovation' in some precincts of the early church. 
Jesus' silence suggests that governance issues were, and remain, things that the disciples — that is to say, all of his baptized followers — could and should work out for themselves. In the Episcopal Church (TEC), we've done that in a particular way, as documented in our constitution and canons.
This is relevant, of course, because the Primates' Communiqué seems to assume that TEC's bishops, as the allegedly-exclusive successors to the apostles in our branch of the church, can effectively bind TEC even if the House of Deputies objects. The Primates don't seem to understand that TEC's sees and dioceses are creatures of our democratic polity of the baptized, not vice versa.
Putting it bluntly: Apostolic succession notwithstanding, traditionalist Primates and their allies need to keep firmly in mind that our bishops work for us, not the other way around.
 Roman Catholics, of course, claim that bishops are the designated successors to the apostles, who as such must govern the church, with Peter and his successors as the supreme leaders. Certainly Jesus had previously told Peter that the latter was the rock upon which the church would be built, and that he had the power to bind and loose sins (Matt. 16.18-19). But that didn't seem to settle the matter of the church's governance: Sometime after that episode, ten of the Twelve got angry because the mother of James and John had asked that her sons be seated at Jesus' right and left hands. Jesus responded to them that whoever wished to be first among them must be their servant — suggesting that the question of leadership of the disciples was still (and would remain) an open issue (Matt. 20.20-28).
 After Judas' death, the remaining eleven disciples made some governance decisions purely on their own authority, with no recorded instructions from Jesus. First, they decided, based on their reading of Psalms, that they needed to replace Judas so that their number would be back up to twelve (Acts 1.15-26). The reconstituted Twelve also appointed Stephen and others as deacons, because they regarded themselves as too important to do the grunt work of feeding the needy (Acts 6.1-6) It's not apparent that the Twelve's decisions to anoint themselves as a self-perpetuating elite — who even before Jesus' death were markedly interested in their own status and positions (see note 1 above) — should be binding on all the baptized for all time.