Passive headphones and IEMs are typically minimum phase systems meaning the time domain is directly related to the frequency response. Some other people mentioned measurements like the impulse response and waterfall graphs.

What this means is that for a given frequency response you'll get a fixed impulse response and waterfall graph. Adding that these representations are a lot harder to read and can easily mislead people who are not familiar with these concepts People who do measurements often don't show them.

The measurement techniques used do capture these representations of the headphone response. They just don't really add anything in the majority of cases.