There were examples of e-ghosts prior to the Crash, however. Alice comes to mind immediately. And it is all but stated that the JackBNimble file from Big D's will was responsible for a lot of the e-ghosts during Crash 2.0. So while I disagree on the point of e-ghosts, it is certainly possible that the coding of one or more of the Big 3 became the basis of the sudden rise of AIs.
As for TMs, I personally like a different theory. Since we see that Resonance is on the flip side of the coin of the Awakened gene (or we assume, since we haven't found it yet), then, as with the Awakened, the potential may have always been out there, but it wasn't until a certain level of wireless technology was present in the area that their abilities were able to manifest. This nicely ties in emerged critters as well. In addition, it helps explain how Mirage created the Otaku. If he simply activated something that was already there, but hadn't had the chance to express due to there being few wireless signals...
That said, the Big 3 might not all have had the same fate. If, for instance, we take Mirage's code to make AIs, Megaera to become a Paragon, and Deus to do something else, that still works. And unless Pax has slipped into the Endless Archive and erased the backups, the original code of all three would still be there, waiting to be uploaded (and she'd have to go and erase the backups again in Deus's case, as she put him back on the matrix to try and dump him into Eliohann's body).