Power is
power,
RMS ratings on drivers and amplifiers exist for a reason.
And that reason is apparently that the people publishing those ratings don't understand there is no such thing as
RMS power. I believe that basing the
power on
RMS voltage and
RMS current measurements results in calculating the average
power rather than
RMS power.
Cable and
voice coil failures are often related to excessive average
power levels over some period of time and whenever you discuss
RMS or average values you have to consider the time variance of the signal. So addressing topics such as heating in a
wire means considering the time varying nature of the signal and not just the
RMS or average ratings of the amp and
speaker. What Chris was referencing is the fact that unlike some other electrical signals, with audio the signal usually varies significantly over time and thus there is typically a significant difference between the peak and average levels or a higher
crest factor.
I'd guess that a cable between an amp and
speaker 'burning up' generally relates to some amp or
speaker failure, damage to the cable,
etc. and that you would be hard pressed to find a situation that would result in 18AWG
speaker cable 'burning up' that would not have the same result if the conductors were 12AWG or 10AWG.