You mean amp, not dac, don't you? Although I accept in many cases they are in the same box.
Many do call their headphone Amp's just "DAC" in most situations when they speak of their headphone output sources, in this case "amps".
So correct term would be the headphone output (amplification) ports with higher output impedance are the source of "coloured sound" when talking about "DAC's adding flavour" to their headphones.
Sensitive headphones when paired with high output impedance amp get coloured sound with the variance of output impedance and why DAC's sound different in the layman terminology of why people are so sensitive about it.
With the coloured sound possible with higher impedance. Which impedance was the "reference" impedance when designing each and every headphone and their correct frequency response?
What equipment was the design paired with?
A low >0.5 Ohm one or a ~10 Ohm or a higher like 75+ Ohm output etc.
So when people compare their headphones & Amp's they need to be aware of the impedance issue. The possibility it can colour the sound of their headphones and have it in mind when they make comparisons & assumptions.
Not all headphones are as sensitive as another. But we have already seen it's quite possible to have a 2 dB range difference for a large part of the frequency range.
That is a audible change of character!
We have basically a passive EQ filter in effect with the variance of output impedance from DAC's headphone amplifiers. Which does have and effect on sound. And why people go on and on about liking one Amp(DAC) over the other paired with their specific set of headphones. Adding warmth or being cold or whatnot descriptor they want to talk about to describe the difference in output.
To be fair the ideal way would be to standardize the lowest possible impedance across the range as the reference but that might not work out. To many players around wanting their own thing.
Variable impedance "setting" as the next new thing to have to possibility to mix & match to your liking what kind of coloured sound you like paired with your headphones, could be a solution but just having EQ settings more widespread would be ideal in the length.
Most people don't know how to adjust EQ other than to taste rather than correcting faults.
Impedance matching your DAC headphone amp outputs would be necessary when doing a direct to direct comparison for the performance of a headphone amp.
Many might like the added colour with the Bass frequency boost with higher impedance if other headphones react the same or similar to the DT 900 PRO X.
Some might not like it and want the less coloured low impedance output sound.
I've never seen talk about the impedance can have of an effect in general from Audio gear reviewers or such in-length at all. They just talk about the end result. Not the cause or source of the change in character. And why they make choices of recommending one DAC over another for your headphones output.
They seem inware of the possible change it has and or dismiss it as irrelevant when it's there in the data & measurements! The sound is measured as different, depending on the impedance!