I found an interesting quote from the book From Jesus to Christianity, by L. Michael White. Commenting on the writings of the early second century Christian martyr Ignatius, he says:
...Ignatius shows little awareness of those writings from the New Testament that would have existed in his day. He shows some limited awareness of Paul and may paraphrase at times from 1 Corinthians, but does not seem to know about the other letters. It is possible that he encountered those Pauline materials for the first time upon arriving in Smyrna. Among the Gospels, he may have read Matthew (see Ign. Smyrna 1.1), although it was not a central fixture of Antiochene Christianity. The scriptures, for Ignatius, are the Jewish scriptures of the Septuagint. On the other hand, Ignatius does seem to know a wide range of early Christian traditions of vaguely recognizable character...Here we see an illustration of the point that, approximately a century after the death of Jesus, the Christian community had no conception of a New Testament; and when they conceived of "scriptures" at all, they were referring to the biblical books of their parent religion.
Thus early Christianity expressed two tendencies with respect to the question of "scripture". On the one hand, believers respected the traditional scriptures of their predecessors. Yet, on the other, they lacked any foundational canon specific to their own, new faith. Their faith was not frozen permanently into a rigidly defined set of words that they would have to turn to as a definitive source for Christian doctrine. They were, in a sense, making it up as they were going along. Yet they weren't inventing their religion out of whole cloth either; they revered traditional scriptures of their predecessors who operated under a pre-Christian paradigm.
This combination of a) respecting prior scriptures, and b) not being bound by such scriptures--because they were in still in the process of creating those canonical works and figuring out what to revere and give special attention to for their new faith--represented a process that was lost once the canon was fixed. Whatever was gained by closing the canon, much was lost as well. This dual process of respect for tradition and inventing new ones represented a process of creative listening that is lost once the canon is frozen forever in time.
There is something to be said for revering the prior scriptures of a previous time and paradigm; there is value in seeing how prior generations tried to get a handle on God. But once you freeze the process and deny the continuing ability of God to speak to us in ways that are just as significant as they were many centuries ago, you shut yourself out of a dialogue with the divine. The worst consequences of this attitude towards the canon are the sins of fundamentalism, with its attendant doctrine of biblical inerrancy. It makes it possible for fundamentalists to claim that all the doctrines, all of God's word, is found in this set of writings many centuries old that a group of religious leaders decided would constitute a canon. If the canon were not so rigidly closed, the idea of biblical inerrancy as well as other notions of fundamentalism would have been much more difficult to justify, in my view. If you conceive of revelation as a continuing process and the "canon" as merely a developing expression of that process, it isn't clear to me how such a fundamentalist bible-idolatry could even emerge.
Yet a further problem with the closed canon is that even some who accept that revelation continues in the present day may also insist that any new revelation cannot contradict whatever was written in the Bible (or in the case of Roman Catholicism, whatever was expressed as official church doctrine.) This gives a rigidity to dogma, forcing believers to accept the infallibility of whatever certain individuals wrote or thought thousands of years ago. Ignoring the problem of contradictions that exist in the Bible, one of the reasons why continuing revelation is important is that many of the writers of the Bible may have just plain gotten some things wrong. They were human. They tried to understand God in the best way they could. But they didn't quite get it all right. They weren't perfect--any more than the people who chose what books were to become canonical were perfect in that decision.
That isn't to say that I don't think there is also value in the familiarity of a closed canon. By referring to certain known biblical passages and incorporating them into worship, rites develop around those passages that can contribute to the worship experience for many people. But I also think it might be worth considering the ways that humans can open up their dialogue with the divine. The United Church of Christ likes to say that "God is still speaking". The Quakers talk of "continuing revelation". These are valuable ways to consider the ever present process of revelation. Revelation did not end with the closing of the canon, nor was the canon an infallible record of revelation. Rather than shutting out this process of listening to God for new insights, let us revel in it instead.