Is phase angle a important thing to consider when designing filters?
From system theory we know that the negative slope of the phase response gives the so called "group delay" of the filter. For some applications - e.g. filtering of squarewave signals - we want to have a group delay as constant as possible (identical to a linear phase response) in order to retain the original waveform (in spite of filtering).

This requirement was the reason to define the Thomson/Bessel response as one of the standard filter functions. As an another example: We have allpass filters (constant magnitude over frequency) with the only purpose to shape/correct the phase response (resp. group delay) of other filter ciruits (Delay equalizer).