I just got around to digesting this at the level it deserved.
There are of course many different wire sizes. AWG 18 wire has a diameter of about 1 mm. I think most of the signal wiring was smaller than that precisely to save weight, but the power wiring would undoubtedly have been much heavier.
True the latter, you have some high-current wiring in the CSM and it takes thicker conductors to pass it. That said, thinner wire saves weight, but also heats up more. In wiring for vacuum, you have to take heat rejection into account. Thinner conductors also break more easily in a high-vibration environment. Most spacecraft are a high-vibration environment, at least for the first 6 minutes of their flight (i.e., atmospheric boost). The LM was notorious for wire breakage in early development shake tests, requiring thicker and thicker conductors to handle the mechanical requirements of the wiring harnesses. Harnesses made from thicker conductors don't bend as easily, requiring redesigning the harnesses and the cable runs that accommodate them. I have some samples of high-bandwidth cabling we can use for digital communications. It has a data bandwidth of 12 GB/s (that's big B for "bytes") but a foot of it is so inflexible that you can hold it at one end and it cantilevers out straight with a cell phone hung from the other end. Designing runs for this marvelous data channel is... challenging.
Of course, part of each wire is the much less dense insulation, probably Teflon.
Variously Teflon, Kapton, or TKT. Kapton is great because it has the best electrical insulation value per unit mass, requiring a thinner sheath and less cross section and mass for the harness. However it has the ugly property of failing to self-extinguish in a high oxygen environment and having poor abrasion properties. Teflon has reciprocal advantages. TKT is a composite sheathing involving an inner layer of Teflon, the bulk of the sheath being Kapton, and finally an outer layer of Teflon again. It's a very expensive best-of-both-worlds product.
That's important because they're still among the most unreliable of all electrical components.
Indeed. Every manner of connector manages to shake loose eventually under takeoff acoustical loads. This is why we still prefer to hardwire everything and then guillotine/deadface it where separation is a requirement.
The reduction in wiring complexity is so great that it becomes easy to add another bus for full redundancy.
It also compensates for the problem that the wiring in a digital bus becomes a critical item itself. With home-run analog wiring, damage to wiring harness gracefully degrades the affected systems. With a digital bus, damage to the harness that implements the bus can fail the bus entirely, failing large portions of the spacecraft. Hence the additional bus (preferably routed somewhat differently) is comforting.
A digital air- or spacecraft bus greatly simplifies recording and telemetry. In a modern airliner, where miles of analog wiring used to prevail, the important (and previously difficult) task of flight recording has been greatly simplified. DFDR aggregators just plug into the bus controller now.