Post-ringing is what makes a musical instrument:
A drumskin, a string vibrating after being hit or plugged, an air-volume or a soundboard of an instrument resonating after being exited etc. etc.
No resonances - no instrumental colors.
So a little extra post-ringing usually stays unnoticed, at least doesn’t sound unnatural.
This is true if EQ isn’t overdone and / or misstuned.
EQ well done even can reduce ringing of a transducer and improve it’s transient response by some amount.
A prerequisite for this is, that the EQ and the transducer work by the same principle, which typically is Minimum Phase in nature.
With acoustical transducers this is only partly the case, as sound reflections of all kind are not Minimum Phase.
It’s easy to find out:
Check what sounds better TO YOU - that‘s the only thing that counts.