time domain spectrum plot or measure the burst response
Spectrum means frequency domain, so mixing that with the term "time domain" doesn't work.
You can transform from one domain into the other and both contain the same information, though in audio FR plots we usually just plot the smoothed magnitude and omit the phase completely... because that is the easiest to understand and FR magnitude is the most important aspect in how a headphone sounds.
"Burst responses" (technically called impulse responses or IRs) are rarely measured directly because of SNR issues, because an impulse contains very little energy especially at low frequencies.
But that's not an issue, as I said you can transform from frequency response (measured e.g. with a sweep or noise) to time domain and plot the IR.
But you need to understand what you're looking at. In other words, interpreting IRs is where it gets tough...
It would be good to know about driver behaviour and how long lived the resonances are.
and where we need to be careful. For example, a lot of people don't know that any deviation from flat in FR necessarily means "ringing" in the IR.
But this does not mean there is a resonance. Even an overdamped low-pass ("slow and smooth bass roll-off") results in "ringing".
Another thing is that this "ringing" usually is not audible as such. You don't hear the ringing at the cutoff frequency of the low-pass which you'd see in the IR, instead you hear the attenuation of lower frequencies, i.e. lack of sub-bass.
So I'd say that for most people such a visualization is not helpful. Even worse, I'd consider it harmful if people started to read magical audio properties out of IRs they don't understand.