They aren't driven by a want of technology. They're on a quest for perfection (and "technological perfection" is only one facet of that.) Even if only one single entity is left standing against them, that would be a thorn in their side reminding the hive mind they weren't there yet. They hadn't assimilated every single being in the cosmos.

Also, they see assimilation as a kindness to the assimilated individual in a twisted sort of way. Maybe even a moral imperative. There are a lot of places where the borg go on about how "you'll never be alone again if you just let us assimilate you."

And, honestly, by "they" I kindof largely mean "she". (Pronouns and sci-fi! Happy June, people!)