Sidebar: IIR vs. FIR
As in most aspects of life, there are exceptions to everything. Unlike IIR filters, the relatively new breed of filters known as FIR can alter the frequency response of a system without altering the phase response.
However, there is a price to pay. Since phase and time are impossible to separate, the price you pay is that any change in the frequency domain will result in a corresponding effect in the time domain, i.e., additional signal delay.
For some applications like cinema or AV track playback, this might be perfectly acceptable. For other applications, such as stage monitors or front-fill loudspeakers in small theatres, even a small degree of signal delay may not be appropriate.
Each situation must be carefully considered and addressed in regard to the intended end-result. And that is exactly the approach that helps us all further our craft.