Ideal transfer function has linear phase with frequency. This means that all components of the spectrum of the signal has equal delay. Group delay is nothing but derivative of phase characteristics. So group delay is constant. Any deviations from constant causes change of pulse shape on the output. Question here is how much shape distortion you can allow. To minimize distortion, flatten group delay, you can implement phase equalization to transfer function (filter). Filters other than Gaussian or Bessel has steeper edge but introduce nonlinear phase responce so they usually have phase equalizing cells at the end.