It appears that William Wrede was an earlier, more important precursor to the "community" approach.
In The Messianic Secret (1901), Wrede criticizes his contemporaries for forgetting that the Gospels are "just a later narrator's conception of Jesus' life." Coming to grips with this fact, Wrede argues, entails paying more attention to the way the Gospels served the needs of their communities:
I should never for an instant lose sight of my awareness that I have before me descriptions, the authors of which are later - albeit relatively early - Christians. These Christians could only look at the life of Jesus with the eyes of their own time and describe it on the basis of the belief of the community, with all the viewpoints of the community, and with the needs of the community in mind. (Introduction, emphasis added)
Of course, this assumption is essential for Wrede's explanation of the messianic secret as an attempt by Mark and his precursors to make non-messianic Jesus traditions conform to a growing belief that Jesus was the messiah, not just after his resurrection, but during his earthly ministry as well.
Given the influence that The Messianic Secret had on form criticism, I think we should look here when assigning blame or credit for the looming presence of "the community" in our exegetical imaginations.