IIR filtering vs IFFT filtering by zero binning and making bandpass IIR filters with high sample rates?
An IFFT of a single non-zero bin (or conjugate mirrored pair) produces a single pure sinusoid (with no phase or amplitude changes).  An IFFT of just a few adjacent non-zero FFT bins produces something like a slowly amplitude modulated sinewave (a beat note) possibly very slowly modulated in frequency.  Note that none of those IFFT results resemble a sinewave that includes a sudden instantaneous phase shift.  The information about the location of a possible sudden phase change is located in all the other FFT bins that an ultra-narrow FFT filter throws away.  e.g. you would have to de-zero a vast number of FFT bins to get that change to reappear in the IFFT result.  That is why sharp changes have very wide-band spectrums.

This renders your proposed filter (zeroing all but a few FFT bins) nearly useless for determining the location of any sharp phase shift.