As far as I have seen, almost all theoretical filter design occurs in Laplace or Z-space. Also, there is a pervasive connection to real life analog filters in the design. If one is just thinking in a mathematical theoretical thing (or something that could be implemented digitally), why wouldn't one filter signals in Fourier Space?
Why is, say, multiplying the Fourier Transform of a certain function by a unit step up - step down function, and then making the Inverse Transform of the resulted signal a "band pass filter"? Why should one use Butterworth filter or similar things to make a digital filter?