But yes, in TNG the assumption was that Borg drones were incubated from infancy as drones and never had any other identity. Picard's assimilation was portrayed as a rare thing. When Hugh and other drones were liberated in "I, Borg" and "Descent," they had no prior lives; they were empty vessels seeking to create identities. Even in First Contact, the assimilations we saw were the result of the Borg being low in numbers after the destruction of their cube and needing to assimilate personnel in order to replenish.
So it wasn't until VGR that we began to see assimilation portrayed as a normal practice. But that wasn't because of Brannon Braga. It began in the third season, while Jeri Taylor was the showrunner, starting in the episode "Unity" written by Kenneth Biller, in which we encountered a colony of former assimilated drones. It then continued in "Scorpion," which was written by Braga and his writing partner Joe Menosky, but still under showrunner Taylor (and, of course, answering to Rick Berman).
The explanation I offered in my TNG novel Greater Than the Sum was that the Borg in the Delta Quadrant had been severely depleted by the war with Species 8472 and thus had to assimilate more aggressively than before to replenish their numbers. True, VGR showed us plenty of drones assimilated before then, but I figured they always used both methods, assimilation and incubation. But they kept the incubated drones in the further reaches of their territory as a rule, because those drones would be less likely to rebel if they were cut off from the Collective.