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Anybody who does anything in the real world with Fourier transforms uses the fast Fourier transform operating on windowed data. This eliminates all of that infinite support and infinite resolution of frequencies.

Yes but they commonly dont end up as FT/FFT. For example wavelets and DCT.

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.

Not sure if an oblaque tomb raider reference or math metaphor.

It's both a math metaphor and a Star Wars prequel reference.

not like here.