From Universal Audio's WebZine:
[Linear phase] delay leads to advantages and disadvantages, depending on the situation. The biggest advantage is gained in filterbank applications, where a signal is split into frequency bands for separate processing, and recombined later. If a filterbank is made to be linear phase, it can be completely transparent as long as no modifications are made to the signal while it is split into separate bands. An application for this may be a de-esser which is being used to limit occasional sibilance. If the de-esser is made with a linear-phase filterbank, it can be made to be absolutely transparent except during those instants when the de-esser is active, reducing sibilance. On the other hand, if the filterbank is not linear-phase, then anything sent through the processor will incur phase distortion all the time, even when no de-essing is taking place. So for transparency in a filterbank, the linear phase property is valuable.
For EQ applications, linear-phase filters will have different properties than their most commonplace counterparts, minimum-phase equalizers, but the advantage is not as clear-cut. Because linear-phase filters delay all frequencies by the same amount, the overall latency for a linear-phase filter will be higher than for its minimum-phase counterpart. Minimum-phase filters, on the other hand, have the least latency for a given magnitude response. This means that linear-phase equalizers can be unsuitable for real-time operation, or for operation within a feedback loop.
G.