To be more precise, when working with sampled data with uniform sample rate you use the Discrete Time Fourier Transform (DTFT), not the Fourier Transform!. None the less, you still end up with an approximate spectrum which is the signal spectrum convolved with the window function's spectrum.

In my view the Fourier Transform is still useful in the real world. For example you can use it to analytically derive the spectrum of a given window.

But I think the parent is hinting at wavelet basis.