You have enough information to perfectly reconstruct up to 22 kHz
No, you don't. You have enough information to reconstruct
A 22kHz signal, which will have the same frequency as the original signal, as per the Shannon theorem. But nothing more. Actually, that signal is so bad and affected by aliasing that modern recording and CD players just apply a low-pass filter to eliminate the high frequencies (usually above 16kHz).
with a dynamic range of 96dB
That's also false. You're confusing power of two scale and real audio dynamic range. Power of two is linear while audio scale is logarithmic. It's the same in photography, the real world dynamic range is a lot shorter than the numerical dynamic range, because you have to process the RAW data through a logarithmic function to make it acceptable to human senses.
And at the bottom range of your dynamic range, you're also ignoring that the floor is not at 0, but at the signal/noise floor. Again, it's like in photography: the last few bits usually only contains noise, hence why you need to sample at 12 or even 14 bits per channel to have good shadows without posterization. And with audio, the bottom of your dynamic range has the same problem, you only have a few bits to express whole range of analog values, and that gives you awful resolution.
Remember, digital implies a linear scale, not a logarithmic one. So if you have 16 bits, you're using 8 of them to encode the upper half of your dynamic range. Then, you have 8 left to encode the bottom half - of these, 4 will encode the upper quarter and 4 the bottom one. You actually run out of bits very quickly.
Once this goes through a logarithmic transform in your DAC, this means you have very few bits to encore a large part of your dynamic range, because you wasted most of them on the top half of the dynamic range (that is flattened by the transform).
That's why you use RAW in photography. One of the benefits of RAW is that it lets you tweak that logarithmic transform.
And that's why the CD started the loudness war. With a resolution as poor as 16 bits, you can't have pianissimo, the resolution is too bad at low volume. So, everything has to be loud. That's why you can't use the full dynamic range on a CD, half of it is bad.
Rarely if ever do recordings use the full dynamic range. Even if they would and you set your volume 96 dB above your room noise floor of let say 50 dB, than that would cause permanent hearing damage.
Dynamic range is not about playing music loud, it's about having quiet passages in your music that are still have high quality because they still have enough bits to encode them. And it has nothing to do with dB - that's a product of your logarithmic transform. Remember, you're stretching a discrete sample into the analog world. You can perfectly chose not to stretch it too much - then, you will have for instance 70 dB max, but you will also have a very precise signal.