[kmill]

Speaking as someone who uses this tensor notation quite a lot: putting multiple objects into the same diagram is what a tensor product is, and a great thing about the notation is that it reveals that a tensor product of two matrices is not an essential object in itself.

If you wish, you can draw a circle around A and B to "factor out" that part of the diagram as a sub tensor product. Here might be a way to show that matrix multiplication is both "tensor product then contract" and "function composition": https://imgur.com/tcCycYj.png (though I didn't give this gray-circle notation much thought).

Think about this: how is it in a product abcd of plain old numbers am I supposed to see the mathematical object ad without putting them arbitrarily close together? (Well, in standard notation, you do put them close together and write (ad)bc or something.)