That said, what I heard was that the peak power rating on a class D amp is more applicable as a rating than RMS than on a class AB amp because of the faster power ramping on a class D amp.
I have never heard this. Are you sure you are not confusing "burst" and "continuous" to peak and average respectively?
The thing with most class-D amps is that they can not sustain high average power output for long periods of time without overheating. Therefore manufacturers can't provide "continuous RMS" ratings for them.
However, musical instrument amps do not drive motors so they don't even need such "continuous" performance and in addition the "music" signal has such high crest factors that momentary "burst" power figures are actually a rather good approximate of the amp's performance in terms of output power.
IIRC, something like an ICEpower module, cooled properly, can sustain its full rated output power for about a minute or two. After that the thermal protection kicks in and starts to severily limit the output power. Naturally you can't give such an amp a "continuous" output power rating but its amplifying your bass, not driving a motor so in expected application this does not matter.
When you pluck your bass the initial transient of note attack may easily be eight to ten times as high as the average signal level. If the amp can produce this momentary "burst" at high power without clipping the rest is easier because in average the amp is not even demanded to produce such high power levels.
There is a lot of unneccesary elitism about musical instrument amps supposedly having to be able to sustain their highest rated power "continuously" and indifinitely and burst ratings being dishonest in some regard. It doesn't work like that.