What counts as a phase anomaly?
If you can see changes in the group delay, then you have phase anomaly. If it is a minimum phase issue, you can fix both amplitude and time domain, as they are linked.
Large phase rotation or abrupt phase shift in the midrange (300-3000 Hz) affects the depth and the stability of the soundstage/image and degrade the overall clarity of the sound.
This is where the best DRC programs excel as they uses both peak, group delay and phase to synchronize the speakers and speaker drivers. It is relatively easy to achieve this synchronization when operating with group delay correction. Then you get an almost constant delay and linear phase and it is "just" to ensure that the corrected drivers peak at the same time. The effect is quite dramatic and can't be had in the analog world.
Fixing the time domain issues does improve the overall sound quality, but I would still argue that fixing the frequency response is paramount.