>If we didn't have associativity, we would need to explicitly bind arrows together, and reaction nodes ≤ could only relate one input wire to one output wire (where those wires were pre/post-bound separately from the relation).

You are probably right and I am probably missing something, but I don't quite understand what you have said above. More specifically, I am not getting why you wouldn't be able to bind arrows using the monoidal preorder law without associativity since monoidal preorder laws only require two wires.

Sorry for being slow... I know that this is probably not important but I would like to straighten the logic behind drawing diagrams so that I don't make faulty assumptions in the future.