I've still got as headcanon the idea that the Borg encountered and analyzed the Biophage, in effect managing to assimilate it (though perhaps not without cost), at some point while their cube was covertly sneaking around the Neutral Zone in the early seasons of TNG.
This would explain why the Borg go from "the ultimate users" described by Q, who seem only interested in the Enterprise for its computer records and technologies, to the "assimilate everybody we can get our hands on" portrayal seen a few years later on in the timeline. The Borg certainly had the capacity to assimilate individuals (by grafting cybernetic parts onto them), but they may simply not have had the means to do so with a quick and easy injection of nanites into their bloodstream prior to some point in the 2360s. So they'd only do it when it was worth the effort and/or AFTER they'd already conquered a planet and were in a position to take their time and do it gradually.
It would also explain why Borg nanites have ridiculous magic bullshit ability to cause cybernetic implants to spontaneously grow in the host's body: they're 'domesticated' Biophage nanites, and if anything their capabilities have been toned down and tamed compared to the 'wild' specimens the Borg originally captured and reverse-engineered.
