The Borg were intended to have a recurring role beyond "Q Who?" in the first place, so again it falls to the writers for not defining them properly.
Those original plans that you and Saquist refer to had already gone down the toilet by the time Q Who
was produced, so they have no relevance to what actually became "the Borg". The incarnation of the concept that we actually ended up seeing in Q Who
intended to be recurring.
And in any event it wouldn't get VOY off the hook. They independently made the decision to bring them back as a recurring villain, so the responsibility to handle it well was theirs.
Making them the massive threat and recurring isn't mutually exclusive.