So what about playback? Does a higher sample rate audio really mean better quality?
Yes, a higher sample rate (all other things equal) means better quality.
But that isn’t really a relevant question. A relevant question would be “sound better”. 22 kHz sample rate would sound better than 11 kHz sample rate. 44,100 Hz sample rate will sound better than 22 kHz.
But this doesn’t mean 96 kHz or 192 kHz audio will sound better, since their higher sample rate just supports a frequency range outside of our ability to hear. But it would sound better to a cat or dog or bat.
So with 44100 Hz sampling and an expected upper frequency of 20 kHz, this means the low-pass filter must start at 20 kHz and have reached a silly strong filtering at 22050 Hz. And that means a very, very, very steep filter - and steep filters will affect the sound quality even below the break frequency.
With 192 kHz sampling, it’s enough to have the filter start at 20 kHz and the filter is allowed to use the full span from 20 kHz to 96 kHz to remove high-frequency components. That’s a much, much simpler task. And it’s they way easier to use digital logic to down sample from 192 kHz to 44100 kHz if you want to make a standard CD from the digitized sound.
But directly listening to audio with 96 kHz or 192 kHz sampling rate does not give you any better sound.