also worth keeping in mind that in natural objects (including speakers/headphones/cartridges) - most (but not all) frequency/phase relationships are minimum phase...
Many (most) frequency response variations both electrical and mechanical have a reciprocal behaviour in the amplitude (size/level) and phase (timing) domaing - whereby by using the relevant mathematical formulae, a knowledge of the frequency response can be used to calculate the phase response and vice versa. - This form of phase variation is called "Minimum" phase.
This means that if you use a minimum phase filter (standard "analogue" filter behaviour) to correct frequency response non linearities, you will also correct phase response non linearities. Your end result will be fully corrected in time, amplitude, frequency.
In digital EQ however, we can apply "linear phase" filters - which adjust ONLY the frequency/amplitude and leave the time domain (phase) alone.
If what we are trying to achieve is corrective EQ to compensate for natural system non-linearities, using linear phase filters is a mistake, as you won't be correcting the phase (time) relationships.
Note: I said most things are minimum phase, there is reason to believe that some of the complex twisting behaviour of phono cantilever styli, are mixed phase - and partially behave as minimum as well as partially linear phase - luckily that type of impact on audio is very minor, and completely overwhelmed by other aspects of a cartridges behaviour, all of which are minimum phase.... and therefore correctable by minimum phase EQ.