Some light hints that may point you in the right direction:
Hint 1
The assembly is a part of a larger machine.
Hint 2
Several assemblies are meant to move side by side in unison.
Hint 3
The square-ish shaped piece is plastic that will wear down and be replaced.
Spot on.
Answer
It’s for pushing mail into an envelope. Three or four of them work in unison to push a stack of papers/inserts into an envelope.
God damn. That’s the hardest one I’ve seen in a long time. Very nice.