> Finally, a realizable filter, whose frequency response is always a continuous function of frequency, must have a frequency band over which the gain drops from the passband gain to the stopband gain; this is called the transition band. The thinner this band can be made, the more nearly ideal the filter.

Perhaps ideal from some mathematical view, but musically, a brick wall filter could sound like shit where a lower order filter would be fine, because in that situation, you need a more nuanced blend of the range of frequencies than taking everything at 100% amplitude below the wall, and 0% above.