Melted PSU wires? From 25-30 amps? Cars may do that because 70A go through single wire. And even those are usually very thick...
Sure, wire size matters, as does quality. A spark doesnt need a lot space to jump over, voltage and amps determine how much space is needed before it jumps. The number of braided wire strands per foot (I think was the standard) counted towards its amperage rating. Some of the old power supplies, if you remember, had some very stiff harnesses, it was hard to bend them. It was a pain in the butt to get the 20/24 pin connector harness to take the right shape. That was because there were a low number of strands in each wire, and each stand was larger to compensate for the same amperage. Now more strands=more amps can be carried, more flexible wire harnesses. All it takes to start breaking down a "higher" strand count wire is one strand to break and start arcing. Something like repeatedly folding a piece of metal in half, eventually it breaks.
Also, wire insulation is not perfect, it can dry and crack too depending on quality, its kind of rare. Cheaper wire might also have thin spots or even a broken or bent strand sticking out, all caused during manufacturing and poor QC.
IF you can reproduce your issue by wiggling wires in your case....