One could read any number of classical works that talk about what it means to be Anglican and find virtually no references to the "See of Canterbury." For example, I’m not sure that the word "Canterbury" appears once in John Jewell’s Apology of the Church of England. If one reads those who articulated the historic understanding of what it means to be Anglican—Thomas Cranmer, John Jewel, Richard Hooker, George Herbert, John Donne, the 39 Articles et al—what one finds is a collection of doctrines and practices: (1) an affirmation of the primacy, sufficiency, and clarity of Scripture, an affirmation of the historic creeds as summarizing the heart of Scripture, an understanding of the church as expressing a kind of continuity with the primitive Catholic Church, and a critique of late Medieval and Tridentine Roman Catholicism as a deviation from patristic Catholicism; (2) certain practices of worship and devotion rooted in Prayer Book worship and the daily office. And, of course, views on the relation between grace and morality, all flowing from and connected to the above. Also, while not a central concern (as it was not a matter of dispute at the time) there are very clear statements about Christian sexual ethics—sometimes in odd contexts, e.g., Jewel’s defending the C of E from accusations of antinominianism, or Hooker’s discussions of why wedding rings are adiaphora but sexual fidelity in marriage is not.
For historical reasons, those who wrote these things were in communion with the see of Canterbury.
But, of course, Anglican doctrines and practices can exist without necessarily being in communion with Canterbury. After 1776, the new American Episcopal Church found it necessary to receive its orders through Scotland. When the Church of South India was formed by the merger of Anglican and Protestant Churches, it was necessary to break communion with Canterbury. And they did so with Canterbury’s blessing.
If one actually reads Cranmer or Jewel or Hooker et al, it becomes quite clear that (as they broke with Rome) they would have had no hesitation to break with Canterbury should Canterbury break with the doctrines and practices which encapsulate the gospel—because the identity of Anglicanism does not lie in communion with an historic see, but in doctrines and practices that adhere to the gospel.
Unfortunately, The Episcopal Church has clearly broken with the doctrines and practices that are essential to the identity of historic Anglicanism, and with the Christian gospel. As such, whether TEC is in communion with Canterbury or not, it is no longer Anglican in any historic sense of the term—because it is no longer Christian. If then, churches wish to continue in the historic doctrines and practices that form the identity of historic Anglicanism, it is becoming increasingly clear that they can no longer do so within TEC.
Unfortunately, there are signs recently that the Archbishop of Canterbury seems intent to be complicit in acquiescing to TEC’s departure from Anglican doctrines and practices (and historic Christian faith) and their persecution of those who try to maintain them. This creates an anomalous situation where, in order to continue in historic Anglican doctrines and practices, it is necessary to break with TEC, and should the ABC continue to acquiesce in TEC’s departure, to break with the ABC as well.
The coming to be of an Anglicanism that preserves the doctrines and practices of historic Anglicanism, but is not in communion with Canterbury, as well as an American TEC that is in communion with Canterbury but has abandoned historic Anglican doctrines and practices is odd, to say the least, but the responsibility for such an anomaly can be laid squarely at the feet of TEC, and, unfortunately, more and more the ABC.
Finally, it also needs to be recognized that the historic meaning of "Anglican Communion" has also changed. Historically, being an Anglican meant being in communion with Canterbury because Anglicanism was coterminous with the Church of England. The Anglican Communion came into existence because Anglican doctrines and practices became international, and there were churches that were not on English soil that believed the doctrines and practiced the practices. If Canterbury’s dallying leads to the split of the Communion, and Canterbury aligns itself with those who have abandoned historic Anglican doctrines and practices (and Christian faith), then (necessarily) but paradoxically, in order to remain Christian, Anglicanism will mean being in communion with those provinces that continue historic Anglican doctrines and practices and not with Canterbury.
*From a comment I posted at TitusOneNine