I think the constraint of using a band limited signal is the big misunderstanding many people have in regards to digital audio.

Yes, you can perfectly reproduce a band limited signal as long as the highest frequency is below fs/2.

But to get a band limited signal from a “real life” signal without any artifacts can be trickier than one might think. Especially when the Nyquist frequency is near the limit of human hearing.

And this is the one big argument in favor of Hi Res audio - moving those filter frequencies high above the hearing threshold.