Emanuel Tov has published a nice piece on the early history of the Torah scroll that describes his take on the origins of the scribal traditions. My main critique is that he follows Haran in supposing that early scrolls only had one book of the Torah, while the complete Torah scroll was a late development of the common era. He understands this as a technological limitation in the earlier periods, but it's difficult for me to see how this could be, since all you really have to do is stitch more sheets on. Indeed, even in the rabbinic periods of complete Torah scrolls, scribes also continued to produce copies of individual books of the Torah. I think you see the same both/and practice in the DSS, so synchronic functional differences seem more compelling to me than diachronic and technological developments.
While I admit that we have no preserved, complete Torah scrolls from the Hellenistic and Roman periods to conclusively demonstrate that complete Torah scrolls were produced at the time, I think the evidence strongly suggests this. Some scrolls indeed only had one book, but many had more. In my study of the Exodus scrolls, fully half of them had concrete evidence for containing more than one book, including the 4QExod-Lev-f from as early as the 3rd century BCE. The large formats of these scrolls were clearly designed to hold very large quantities of text, and even if they contained the entire Torah they would still have been significantly smaller than modern Torah scrolls, so we can hardly discount the possibility of such scrolls. Tov says that maybe these scrolls contained only two books, but other than the much later Rabbinic prohibition of this practice, we have no evidence that this was ever done in the earlier periods. So why discount half of the DSS evidence based on an unattested alternative possibility, rather than simply prefer the more likely explanation that the DSS (just like rabbinic literature) evidence both scrolls of individual books and Torah scrolls?
In a forthcoming article, I do suggest a possible technological development that could have prompted the creation of the Torah scroll, but at a much earlier period. I have observed in a COMSt Bulletin article that the Hebrew/Aramaic script decreased in size significantly in the Hellenistic period (3rd century BCE), making it possible to fit much more text onto scrolls. I think this is the most likely technological impetus for the creation of the Torah scroll, and it is no coincidence that we see evidence for this already in the earliest of the DSS. So it seems to me that the Torah scroll has even deeper roots than Tov is willing to concede.