No spec applies perfectly to any signal. Am I running a midi driven synth rig with tons of compression? Continuous power is probably pretty applicable.
Am I using a normal electric bass, playing classic rock? Continuous power isn't very applicable.
...but applicable or not, continuous power tells me (as an electrical engineer) some very specific things about the overall capabilities of the amplifier.
Plus - don't assume I'm only going to use a bass amplifier for bass. It could be used for keyboards, or PA, or any number of other things depending on the situation.
What if I'm running pure sin wave synth signals through my PA amp? Doesn't sound at all "out of bounds" to me.
Well then, since we are designing the product specifically as a bass amp (not a keyboard amp, not a sine wave reproducer, not a vibration table driver), the most applicable approach is to consider the type of signal consistent with its intended application. Along with this, if you are going to reproduce sine waves with your speakers, you might need to consider derating many of the speakers on the market that otherwise make outstanding bass guitar speakers, because they are designed with a different and clearly marketed application in mind.
I am going to assume that a bass amp is going to be used with a bass. If it isn't going to be used for bass, it's up to the potential user to determine how suitable it is for their particular application. This doesn't just apply to duty cycle, but to input impedance, input sensitivity, high pass filtering, etc.
For bass guitar, continuous power isn't going to give you any additional information specific to the application. Knowing the duty cycle certainly will (and this is something that I have in fact discussed and provided in the past). As an engineer, I presume you would understand why continuous metrics do not apply to non-continuous signals.
Now I do feel that defining the measurement metrics in RMS terms does in fact tell you something, as peak power is nothing more than a mathematical conversion of the same measurement into a different numerical value that is always higher by a factor of 2 (for the RMS to peak conversion of a sinusoidal type wave form). Of course, all this does is piss off the marketing folks as they come form a "bigger is better even if it's exactly the same thing" school.