Illogical circumstances, in a time travel story? Say it isn't so!
What makes you think that the Borg even could go back to that point in time, that far back? IIRC, the only instance when any species in Star Trek has gone back that far is when Q took Picard back in "All Good Things...". Q is godlike. Are the Borg godlike? Are the Borg to exist without limitation? Are we to suppose that the Borg's journey back in time was something that they could perform without risk to themselves? If that were the case, why wait to do it as an apparent last resort, when the cube was being destroyed?
Also, there's no way that the Borg could have been smarter than any group of 20th-century writers, no matter how inspired they could have gotten. I'm afraid we're just going to have to settle for living in reality regarding that.