The measurements on this forum seem to be very much about what is produced when an ideal signal is fed in - e.g. a 1KHz sine wave. Its good to have a reference point but what happens when you feed a real musical signal in?
Two things. IMD and masking effects.
Yes, IMD is a real thing, but it's also being tested in the reviews here on the site. So far I haven't seen any indication of it being something worth worrying about.
Masking effects, on the other hand, works in the opposite direction, meaning that the "complexity" of music isn't really doing us any favors in terms of detectability.
The more "musical" a signal gets, the more it covers up the sins of noise and harmonic distortion.
1kHz is really a best-case scenario when talking about detectability. Both because it's a single tone, and because it sits smack in the middel of the most sensitive part of our hearing.
Do different DACs respond differently to different frequency mixes and sudden changes to the frequency content of a signal?
A sudden change is an impulse, and an impulse response is technically the same as a frequency + phase response. If those two show no issues, you're in the clear.
Not to mention that the "sudden changes" that people imagine happens in music isn't anywhere near as sudden as they think.
Even if you want to reproduce the cannon shots of the 1812 overture more realistically, the SPL capabilities of your speakers becomes infinitely more important then the impulse response of your electronics.
For example, are there any tests that have a baseline piece of music that gets fed in and then the output waveform is measured and compared - If you had very similar measuring DACs from the sine wave perspective would they all end up with identical wave forms coming out when actually playing music?
You could try a null tester. I bet all you'll hear is a bit of noise. Probably comparable to a few more insects doing their normal business in the small cavities of your home.