In order to get a better feel for phase response and how it applies across the field of dsp, I'm looking for example scenarios where a filter's phase response is a concern and where it is not.
Take for example the attached figure I've made. The graph compares an analog RC low-pass filter (S) with both its digital IIR conversion (RC) and the Exponential Moving Average (EMA). It is based on a samplerate of 16 khz. I'm including both the phase and magnitude responses, as it seems quite evident that only having one would tell only half the story.
The EMA's phase response notably deviates from both RC filters at 1/80 of the Nyquist rate, or in this case ~100Hz.
When and why might this phase response be an issue, and when not? I ask to better understand how to consider phase response when implementing filters.
While audio is a notable interest of mine, I'd like to be shown examples across the dsp field, mundane or elaborate and everything in between, is welcome.
P.S. not to be off topic, but any tips to improve my graphs would also be welcome in comments.