[lxgr]

A sine wave is a sine wave; it can't contain any "additional information" that would gain anything from getting encoded by more data points.

If it would, it wouldn't be a sine wave anymore, and you could decompose it into its component of phase and amplitude shifted sine waves, which will occupy all kinds of places in the frequency domain, many of them higher than your initial 22 kHz.

That's in fact what we mean when we say "a 22 kHz signal": An ensemble of all of these overlapping waves represented as a single signal. If you're sampling that with an ADC, you're not only sampling the the 22 kHz wave, but you're also sampling it – and that, but only that, can in fact be described with a single bit per ADC readout.

Looking at it from an information theoretical point of view, the Kolgomorov complexity of "a sine wave of 22 kHz and amplitude x" is pretty minimal – just from that sentence, you can perfectly recreate that signal with no sampling whatsoever, and one ADC readout tells you its amplitude and phase. It can carry a bandwidth of 0 Hz.