Andy - 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.
Thiel wire is very good. In fact, Thiel "found" wire as a design variable in the development of the O3 in 1978 and introduced aerospace wire to the industry. All models of Thiel wire is, and has always been since that time, 99.9999% pure, low oxygen, long crystal copper developed originally by ITT for the space project, and since then cloned by many makers around the world and now improved by continuous casting and other advanced technologies. I'm guessing that Thiel wire trumps all but some of the highest cost and/or DIY speakers out there.
Although various configurations are appropriate for hookup wire, Jim chose 18 gauge solid in teflon @ 2.5 twists per inch as a well considered judgement of maximum versatility. Economy of scale was a major concern - good wire is very expensive and big order quantities reduced cost, so all hookup wire is the same, and therefore might stand upgrading via specific-use engineering. More on that in a minute. Beyond hookup wire, the same quality criteria apply to coils. The signal meets hundreds of feet of series and shunt coils inside the speaker. Thiel uses 6-9s copper coils, tightly wound and oven baked. Great coils. In Thiel's and third party testing, our wire and coils are best-in-world performers.
However, it's never that simple. In the present XO upgrade project I have learned that later speakers including 2.4's were supplied with Chinese-made crossovers. The copper (and other parts) is supposedly a clone of Thiel Copper, but it is not certified and my research causes me to doubt the claim. The coils are obviously lower grade manufacture as learned from Beetlemania's work on his 2.4 upgrade project. The resistances and topologies of the wire and coils are all good, in fact the coil values have been tweaked to account for inductive changes with Printed Circuit Board mounting. The XO performs properly, but sound quality probably suffers a little, as ascertained by Thiel insiders.
My plan is to evaluate the source of each XO encountered to decide whether to keep or replace particular parts. Beetle's late 2.4s have every element replaced. My 2.2s keep all coils and French-film PolyPropylene caps and German Styrene x Tin foil bypasses. My PowerPoints include a Lex and a China pair. Lex are better and will retain some parts. No China parts are being reused. It's a riddle which I am systematically solving.
Another element is wire gauge. Lower resistance is the primary reason for larger wire. However, the overall circuit resistance from input terminal to driver lug is measured and accounted for in the XO, so resistance considerations become nearly insignificant. Our upgrades are increasing some (woofer) hookup wire diameters for greater ion flow optimization. Coil gauge is only changed where required for foil cap upgrade availability. Contrary to some opinions, the small gauge shaping coils are superior to larger gauges, because they can be tuned to their parallel resistor for balanced resonant circuit performance.
I am accounting for wire and coil resistance changes, which may sometimes require a resistor value tweak for proper system performance. Project process is being made. We'll have more to report when the Thiel Audio bankruptcy settles.