Yes in fact none of those are able to catch fast percussive peaks, those are the louder part of the signal, think the attack of the drums hits. Also, I don't see a setting to change the weighting. Typically they are a-weighted when the goal is to assess your listening level, which is what matter most. A-weighting means that if a bass note register at 80 dB SPL which in reality is 80 phon, your amp is developping almost 120 dB SPL at 20 Hz and and 100 dB SPL at 50 Hz, due to the equal loudness contour curves. These are great tools to assess your listening level which is what matter for safety and for setting comparison levels with tones and many more applications, but it is not the right tool to calculate how much headroom, and by extension how much power, is necessary for reproducing the full dynamic range of a recording without clipping. This requires some math and you will also need to know the crest factor of the recording you want to reproduce. I won't be able to tell you if this amp has enough for you.
I think we may have derived from the subject of this thread. There is a full discussion here for more deeper insight:
https://www.audiosciencereview.com/forum/index.php?threads/amplifier-power-how-much-do-you-really-need-and-your-system’s-dynamic-range.22714/