On the matter of “amplitude only” correction with REW or other tools : even though they are not linear phase and cannot correct speakers with time alignment issues, they can be acceptable in the time domain within certain limits of group delay at given frequencies (group delay is the first derivative of phase over time). Typical thresholds are given by the Blauert and Laws criteria, see here of Google Images “Blauert Laws criteria” for the graph.
To check the group delay of your filter (for example a .wav generated by REW EQ), import it in REW, with a drag and drop or File / Import / Import Impulse Response. Then select the “GD” tab and check if you’re below Blauert Laws criteria.
Here’s an example of a correction I use in my living room.
