But we tend to ignore high-frequency data's specifics most of the time, so it psychologically works.
I often wonder though, what do my cat and dog hear when I'm playing compressed music? Does it sounds like a muddy phone call to them?
Likely no.
Audio is decidedly less "compressible" in human perceptual terms. The brain is amazingly skilled at detecting time delay and frequency deviations, so this perceptual baseline likely extends (mostly) to your pets.
You can fool the eyes a lot more easily. You can take away 50%+ or more of the color information before even a skilled artist will start noticing.
since some species use their auditory systems for spatial localization, i would guess that the perceptual system would be totally different in those contexts.
Another aspect is time resolution. Song birds can have 2-4x the time resolution of human hearing, which helps distinguish sounds in their very fast, complex calls. This may lead to better perception of artifacts in lossy coding schemes, but it's hard to say for sure.
Edit: reference on cat hearing: https://pubmed.ncbi.nlm.nih.gov/4066516
The hearing range of the cat for sounds of 70 dB SPL extends from 48 Hz to 85 kHz, giving it one of the broadest hearing ranges among mammals.
Sensitivity to different frequency ranges is more or less independent of anything else. Birds have heightened frequency response in the range they vocalize in, which helps them hear others if their species. Same for us; we vocalize at relatively low frequencies, so most of our hearing ability is focused on that range. There is also a range below which we don't hear: infrasound, which is utilized by elephants.
Logarithmic perception is certainly real, but the tuning of which frequency ranges an animal is more or less sensitive to is certainly species dependent.
-via Wikipedia
This holds true for most other audio compression as well.
Now, it's true that max recording frequency is bounded by sample rate via the Nyquist theorem, but that doesn't mean we're incapable of recording at higher fidelity - we just don't bother most of the time, because on consumer hardware it's going to be filtered out eventually anyway (or just not reproduced well enough, due to low-quality physical hardware). Recording studios will regularly produce masters that far exceed that normal hearing range though.
instead perceptual audio compression typically filters out frequencies that neighbor other frequencies with lots of power. deleting these neighbors is called perceptual masking and to the best of my knowledge, we do not actually know if it works the same way in animal auditory systems.