internal wire is definitely a factor. It carries a slightly different set of requirements from external cable, which must cope with many unknowns of run length, electromagnetic environment, speaker impedance fluctuation, and more. The internal wire is engineerable to the known requirements of the speaker where it is installed.
I agree. For most cases, the internal wirings are much shorter than the external speaker cables, therefore I think it is less likely to modify the signal phase and amplitude vs. the external cables. Some of the expensive speaker cables nowaday I have seen have rather sophisticated geometry and dielectric core material and grounding that together act like a transmission line to deliver the signal as uniformly as possible across all frequencies. Some people think that audio frequencies are too low to be affected by transmission line but I do not think so. Some lesser cables may have resonance issues and the effect is exacerbated as the length increased.
Some believe that the only difference between cables is the resistance. I think it's more than that. You also have the effect of inductance and capacitance - the longer the cable the worse the effect. A perfect cable should deliver the signal from the amp to the speaker input with a constant phase and constant amplitude losses across all frequencies, but since there is no perfect cable (or is there?) by the time the signal arrives at the speaker inputs, the phase and amplitude will be affected differently vs. frequencies. This affect materializes itself as a form of jitter (although there is more than just jitter) A good cable has better phase and amplitude uniformity compared to a bad cable. Some speaker cables are engineered to intentionally have a transmission line affect so the signal phase and amplitude can be better controlled by the designer. With twisted pair, the number of variables is somewhat limited by the wire gauge size and number of winding per in. therefore it may not be able to optimize signal transmission.
In some speakers, the xover boards are located at the bottom so the wire to the tweeter could be as long as 3ft. At that length, there could a transmission line like effect that may modify the signal phase and amplitude non-uniformly vs. frequencies therefore the quality of the cable is more important. But I have personally seen that something as short as 1.5ft length could make significant difference with quality cables.
Anyway, I don't mean to make this into a cable thread (I don't want prof to loose his sleep :-).