[lisper]

It is a tautology. The heavy lifting is being done by the phrase "whose interactions correspond to some basic constraints". Maybe the word "basic" implies more simplicity than is warranted, though if you actually write down what the constraints are, it's a short list and they are not very complicated. That those constraints lead to the tensor product is tautological. I'm not saying this is a Deep Insight, only that it is the answer to "Why the tensor product?"

BTW, just because something is a tautology doesn't mean it can't lead to deep insights. Darwinian evolution is a tautology too: if you have a variety of self-reproducing systems, then the ones that are better at reproducing will make more copies than those that are worse. Well, duh! That's what "better at reproducing" means! The thing that makes it a Deep Insight is that this tautological observation can actually explain some very complex data. Likewise, that the tensor product is the mathematical construct that describes linear interactions between systems that obey conservation laws is a tautology. What makes that a Deep Insight is not that, but the fact that the resulting relatively simple math makes surprising predictions (entanglement in particular) that turn out to be confirmed by experiment.