wire size does limit fault current as does anything that increases resistance and impedance. in fact I have solved more than a few fault current problems by adding a meter or two of wire. Yes I have seen a job with a 24 KA avaialable fault current that would have needed a 42 KA main breaker but by making the service conductors 1 or 2 meters longer wire we got the fault current below 22 ka. This turned out to be very simple as the original fault current calculation was made with shorter wire than was actually needed.

Reno
the tree parallel is more accurate than you think for fault current too.

One of the things we try to do is ensure the fault current is high enough to trip breakers in their instantaneous range. This can require at least 60 amp fault current for a 15 amp breaker or 6 times the breaker rating.
Every wire size has a damage curve and it is very important to open the O/C device before damage occurs. Without some research i think a #14 can carry 300 amps for .01 sconds but I doubt the wire would pass that much current for even that long.