I have bought a sound card that supports 24bit/192kHz sampling (E-MU Tracker Pre), and it is not exactly a new technology: this family of semi-pro sound cards is 10-15 years old. Why is this higher fidelity standard not supported by any website? Is it an underlying limitation of some web standard?
Human ears are at their highest sensitivity level in the early teenage years. After that, it is all downhill in terms of what a human can hear.
The highest audio frequency a human can hear across their lifetime is about 20kHz, give or take a few hundred Hz.
It is true that audio data is captured in samples, and a naive way to view that sampled waveform is with a stairstep-type of a curve, but that is not how audio is stored. The gaps between samples is undefined, and is not defined as the nearest or most recent sample value. This means that when the original waveform is restored from the sampled audio, the only possible solution that fits the sampled audio points is the original audio itself. Bits per sample only changes the noise floor of the signal.
Audio is weird in this way. 44kHz 16-bit audio is capable of capturing any audio waveform that a human being can hear. There probably are exceptions to this rule who can hear, possibly, up to 23kHz or 24kHz audio, and there would only be a couple dozen of these people on the entire planet, and it is likely that they would not know how exceptional their hearing is.
The question of the available higher sampling rates are most often used at the recording stage, to capture the highest quality possible. And 'highest possible quality' will of course depends on your microphone.
In reality, the general public does not have access to such powerful internet services so companies rely on compression codecs to supply things like 8k TV, and other media with high data rates.