Well, Joe gave us the engineer's eye view, and I think I can guess where that is going. His post has spurred me on to write this slightly different take on things.
To me the key issue rests in accounting for the peculiar structure of the textual evidence, the data concerning the textual streams. The process can't be 'normal' in some sense of the word, because we have an essential dichotomy, a bifurcation if you will as per Chaos Theory.
On the one hand you have a well-defined, crisp and relatively non-variant text, which is stable over a period of nearly 800-1000 years (the Byzantine). On the other you have a text that is a little wilder, a significantly less stable, less clearly defined, and having its 'text' appear more as a vague cloud of shared readings among a woolly, loosely grouped cluster of manuscripts (the Alexandrian). They come from different time-periods, and are completely different in nature and quality.
Physicists have to confront such asymmetrical situations so frequently, they have developed a whole group of theories and concepts falling under the category of "Symmetry Breaking".
The idea is simple. Some situations and processes are by nature "stable", robust and predictable, whether steady-state (unchanging), oscillating (cyclic), or progressive (evolving).
A good example of a simple, predictable process might be the slow melting of ice, or a marble rolling around the rim of a shallow bowl toward the center. The process is smooth, and progress can be timed and predicted with reasonable certainty.
A "symmetry Breaking" process is different: Its inherently unstable, and worse, its unpredictable in its particulars. Consider for example, a marble, balanced on the tip of a cone. However long it stays there, we know that at some point in time, a relatively instantaneous change will take place: the balance will fail, and the marble will come rolling down the side of the cone. The problem is, while the geometry of the cone and marble are symmetrical, we have no way of knowing or predicting which way the marble will tip and roll, be it North South, East or West. Some outside force, some jostle, or quake, or bump, will bring the marble tumbling down. But who knows where it will roll.
If the textual transmission were a purely 'normal' process in the sense that Wilbur N. Pickering and friends pose in their book, The Identity of the New Testament Text, (online here), there would be no Alexandrian or other text-types at all; no bifurcation, no abberant manuscripts, no odd clusters of readings or groups of manuscripts.
The text would be copied and evolve randomly and gradually in small steps, through a very long and diffuse process, with errors fairly evenly spread among all the manuscripts. Even local catastrophes (slaughter of a local church, destruction of a scriptorium) would get dissipated by diffusion and mixture, through creeping and cumulative errors.
Pickering himself poses two simultaneous processes acting in parallel, one 'normal' transmission, and one abberant or unusual one. In his model, you have a sedate and stable evolution of the text in the 'normal' stream (Byzantine), with wild, jumpy branching of various isolated local texts accounting for the early diverse witnesses, - an 'abnormal' stream (Alexandrian/Caesarian/Western).
His opponents, supporters of the Alexandrian text-type, would also suggest two separate main streams, only they would pose the Byzantine as the 'abnormal' (corrupt) stream, notwithstanding its uniformity and stability, and the Alexandrian as the 'normal' (purer) stream, in spite of the lack of uniformity of its witnesses.
In either case, some kind of catastrophic "symmetry breaking" event must have taken place to account for the separation and disparity between the two text-types.
Pickering poses a wild, uncontrolled side-process to account for the Alexandrian, while the Hortians propose a 'recension' artificially imposed upon the stream to create the Byzantine.
Both parties seem to agree however, that an 'abnormal', symmetry breaking, bifurcating process has affected at least part of the transmission stream. Each has taken opposite horns of the dilemma, but they both account effectively for the division and difference in nature of the two basic texts, within their own models of textual transmission.
The demonstration of who is right, and who more accurately describes the textual stream is open, without careful deduction. The earliest evidence from the time these processes began is for the most part missing, with only tantalizing but tiny fragments surviving from the early critical period.