Technology could allow you to store (almost) infinitely big (samples/sec) and infinitely deep (bits) data, and in fact lots of things do store this sort of thing: there's plenty of cameras that can record faster & higher detail than human eyes can see, for example 500 frames per second. Likewise there's scientific instruments such as seismometers which are (simplistically) a lot like microphones but far more sensitive than the human ear, and the recorded data is probably stored in more detail than a human could directly interpret if it was played back at real-world levels. However, these various devices are almost always used to capture things so we can analyse them in some other way: a wave on a graph, a slow-motion video, etc.
Going back to audio recording & playback, again there are scientific & test instruments which can sample, record, reproduce & generate far better quality (as in resolution/depth/accuracy) signals than humans can process, but there's not much point in having them in a recording studio.
Now, in a really good multi-track studio you might want better quality than humans can discern as you are adding lots of things together, so the less error you introduce the better it'll come out in the final mix. Simplistically again; if you do all the hard sums using 4 decimal places your final answer may only need to be to 1 decimal place but might still come out better as you won't have lost as much in rounding errors.
In the final case (human consumption) there is only so much humans can discern so equipment is generally made to be good enough for that, because why would you do more work for no gain?
As an example: digital imaging has topped out at 8-bits-per-colour because the eye can't distinguish more than about 256 shades of grey / the total combination of 16.8 million colours & shades. We have 64-bit PCs and much better digital cameras these days, we could store 16 bits per colour, but people can't see 281,474,976,710,656 different colours and we'd waste a lot of effort capturing & storing that data.
Likewise, no-one will pay for a recording studio full of equipment that can hear, capture, record, and reproduce a fly farting at the back of the room over someone bashing a drumkit as no-one will ever hear it, even if it's there.