The ground wire on a phone system is there to keep the chassis and telco leads at a reasonable voltage under various fault conditions. For faults to 60 Hz 20 amp circuits, a #10 wire will have no problem clearing a breaker, and additionally the chassis will not assume a hazardous voltage during the event. The 24AWG or 26AWG wire will light up like a fuse. Lightning transients are a different story. A year or so ago I did some testing on various grounding and cable bundling schemes. What I measured then, and verified just minutes ago, is when you take the level of lightning surge that is within limits where high quality telco equipment is not expected to fail, and where #26 AWG wire is not damaged, the chassis will take a significant jump in voltage. Suppose your equipment has just one four-wire interface that clamps overvoltage to ground, and the lightning surge present is 2.5 KV 500A per lead (per Telcordia GR-1089) with a 2 x 10 uS waveshape. The equipment will route the 2 x 10 uS 2000A (peak) surge to ground. The voltage waveform measured across 12 feet of #10 stranded wire to ground is approximately 1200 volts peak and about 1uS x 3uS, dropping to zero at 5 uS from start of the surge and then going negative to about 350 volts (from the inductance of the wire). This is what would be seen on the "grounded" chassis of the telco equipment if it has outside plant wiring and a line gets hit with what is considered a survivable transient (survivable to your equipment that is). If the system has internal phone lines that clamp to this ground, then they will also see the sudden bump.
For PBX systems that are only grounding internal wiring, and not also providing ground for outside plant circuits, the applicable surge level is significantly less (1500v 100A per lead). I have not ran this test with these lesser surges.
The problem with the #10 wire is the inductance. It is better to use a wide braid, bus bar, shorter wire, or bigger wire (#6), but there will still be some movement of ground under circumstances that do not damage normal telco wiring.
(I was rather surprised at these results back when I first did this testing. I'm now more careful about leaning against "grounded" metal when doing lightning tests.)