The clarity is in the recording production and mixing, and higher bit & sampling is key to recording and production. When tracks are mixed, the "noise" is multiplied, and hence the super-high signal/noise ratio of 24 bit recordings is important for the recording and producing/mixing process, just not for playback (if/when the production is done right). Often, 24/96 bit releases are just better productions than the 16/44 version, while the same is true for LP releases. LP's don't sound inherently better than CDs, but the production on the LP is often better than the CD. In fact I wouldn't be surprised if 24/96 releases were just the LP mix in digital.
With CDs, producers use psychoacoustics (aka "volume wars") to entice the casual smart-speaker listener, while the audiophile gets an earful of awful production. With LP's, producers have tried various gimmicks in the past (like fake stereo), none of which worked. Ironically, it's the inherent limitations of the LP format (no volume wars are really possible) that make the LP often sound better.
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