Speaker wire is also larger because it is "stranded" rather than solid. This allows for easier wire-runs. If you look into the skin-effect, you can lower resistance by having more skin surface area. This allows for runs of wire that have less of a statistical chance for creating their own filters, by lowering resistance, while having the mechanical ability to be routed in tighter spaces with sometimes odd angles. It typically uses thicker insulation to handle higher current. Those are pretty much what makes the cable "in whole" thicker.
As mentioned before, the resistance of the wire and the voice coil in the speaker create a frequency filter. The less resistance, the less overall distortion of the original signal while having enough mass to reduce resistive heating. (Which also increases resistance and compounding the filtering issue)