I'm pretty sure thicker wire (ie. heavier gauge) will carry more current.
The reason you will not see servo wires use for batteries is that they cannot carry the current that is drawn from these batteries. The servo wire will literally burn and melt if 30A is drawn from it by the motor.
Wire length is what increases resistance but only if you are comparing against same gauge wire.
ie. 1 cm of 12 gauge wire will have less total resistance than 10cm of 12 gauge wire assuming a series
Hence the reason why most pro's tend to use as short a wire as possible.
However if you are connecting wires in parallel
which is what I think trf racer is suggesting, you can simulate a thicker gauge wire. Thus the resistance is reduced.
If you were to connect them in series
, it would increase the resistance of the circuit.
Having said that there is also a weight aspect that may negate any benefits gained by adding more wires in parallel, not to mention it can make the wiring look like a mess.
Do a search on google for an explanation of parallel circuits and its effect on resistance for a better explanation