The next confession is that I don't really plan to answer that question. It's an interesting question, but I don't have answers to it. I have some rudimentary notions of where the answers my lie, but it really needs to be explored by serious analysts of science, not an occasional blogger. Perhaps some of the answers are already out there. Books such as Kevin Davies' $1000 Genome skirt around the subject, though I suspect the mountains of material that didn't make it into that book would cast some light on the subject.
In addition to being an important question, I think it is one important to ask now, before memories of the process are completely jumbled. I recently got into a minor tussle on LinkedIn over the history of the human genome project; my recollection of certain events was quite different than my correspondent's (or actually, the other way 'round -- I was challenging his version of events). In a similar vein, I've already had one acquaintance lament that Lynx got too little credit for its contribution to Solexa. Speaking of poor memories, I recently saw a presentation on the web on Manteia, but can't find it again (After posting this, I found it!)
In any case, there are a number of key areas which I think should be explored. There was clearly a major technological shift from capillary fluorescent Sanger sequencing, which was dominant for around a decade and had succeeded very similar slab gel and radioactive Sanger, to a set of radically different technologies. The 'next generation' label is problematic in the same way 'post-modern' is (what comes next?), but second generation has its issues as well since then there is the question of what constitutes 'third generation' and so on. The technologies that first arose to in the space had many things in common yet were each distinct, but they were far more like each other than like the Sanger technology that preceded them, in particular because they resolved sequences as spots over time rather than bands on an electrophoretic gel.
One explanation of the rise of that wave of Sanger-successors could be that the right ideas were simply percolating around. A number of groups, seemingly independently, came up with very similar ideas. In particular, the ones I am a bit familiar with are Manteia in Switzerland, the work in George Church's lab and the 454 story. The Church angle is remarkable in a special way, as when I left the lab in late 1996 the talk of new sequencing technologies were around nanopores or highly-multiplexed Maxam-Gilbert sequencing; yet less than 3 years later the first 'polony' paper was published. I remember some talk of 'sequencing by synthesis' back at some of the mid-90s Hilton Head meetings, though I don't remember any concept of clonal amplification then.
Another class of explanation would be around money. Manteia went bankrupt, and some of its core technology had come from a prior bankrupt company Mosaik. I was approached in 2000 about joining a to-be-formed company to commercialize the polony technology; that company never got off the ground (I find it a bit amazing now that I didn't leap into it; lucky I didn't!). Somehow, 454 was kept on by Curagen until it was ready to launch. On the public side, my memory is that even before Celera a conscious decision was made by the public project to deemphasize sequencing technology development; might a new generation of sequencing arisen sooner if that decision had been different? While we can't actually hit rewind, it is an interesting point to ponder in the context of public support of new technologies.
Yet another area to explore would be the critical contribution of developments outside the field. In particular, all the first round of replacement technologies relied critically on imaging and image processing. Could a technology like 454 have been remotely feasible a decade earlier, given the expense required for the computational support? How critical were advances in microscopy? Or were the key advances in the molecular biology? For example, 454 couldn't have happened without the prior development of pyrosequencing.
Perhaps another profitable area to explore are the technologies that didn't happen, or didn't quite happen. Lynx's technology had many aspects of the second generation: clonal populations interrogated serially. Back in the 1990s it seemed like a logical path was to simply build bigger arrays of even smaller capillaries, or perhaps even lab-on-a-chip-Sanger. Did those approaches die because they were truly dead ends, or did they starve of attention until too late?
I think exploring any and all of these could inform future technology development, and in any case would simply be fascinating. Of course, some of the competing technologies may still arise. Electron microscopic DNA sequencing was discussed in the 90s, and still remains an area of interest. I'm starting to be optimistic that some sort of useful nanopore device will hit the market next year, though whose nanopore and how useful (and for what) remain very murky. Who knows? Perhaps a microfluidic Sanger chip will storm the market?