What is sound output delay of a band pass filter at different freqencies?
The lower the frequency, the longer the period of oscillation.  In any filter using memory (IIR or causal FIR), the filter will have to evaluate a signal for a longer period of time in order to gather information about the same number of periods of a lower frequency signal component than for a higher frequency signal component.  And a filter can't filter a particular spectral component unless it has gathered enough information about that spectral component to "know" whether that particular component is in the stop-band or pass-band, which takes longer (other factors being roughly equivalent) for a lower frequency signal component.

Or you could design a linear phase FIR with the same delay for a lower frequency bandpass, but since it has gathered less periods of information about that lower frequency, it's quality of filtering (width of the transition band, etc.) will be less.