EQ. is useful as a tool not as the only solution , only a part of it ...
The phase relationship is potentially or actually compromised for a reason very deep not many understand well : human hearing was shaped and trained and biased in a certain way by evolution and live in a non-linear time domain of his own which cannot be reduced nor perfectly captured by the linear Fourier tools using abstract concepts which are linearly related (frequencies,amplitude and phase among others) and cannot describe COMPLETELY some aspects of concrete experienced qualitative sound qualities which are perceived in REAL time in specific environment ...
It is why it was proven that hearing beat the theoretical Fourier uncertainty limit more than 10 times times for trained musicians ...
Then you are right there is a trade-off here using EQ. which can be a benefit for sure as any tool but also an impediment or a mask for other acoustic problems waiting to be solved otherwise ...
I then concur with this sentence :
Has anyone mentioned the elephant in the room? Eq’s destroy the phase relationships in the signal. There can be rare times when the benefits outweigh the downside.