I think the blob interpretation, where the bends can be removed and all the strings can be combed straight and have the arrows point in the same direction is incorrect.

Consider what I'm going to call spider profunctors,

\\[
S: X\_1 \otimes X\_2 \otimes X\_3 \otimes \cdots X\_n \nrightarrow Y\_1 \otimes Y\_2 \otimes Y\_3 \otimes \cdots Y\_m
\\]

I conjecture that there exists an arrangement of spiders and loops that can't be undone and "combed straight" as it were.