I’m not exactly sure how you came up with the claim that digital hard clipping isn’t audible. Digital hard clipping is audible!
Also, loudness and the amplitude of inter-sample levels aren’t necessarily related; there’s plenty of ‘reasonably-loud’ material showing +2/3dB inter-sample values. High inter-sample values are more connected to high high-frequency transients — which loud music may have, but so does reasonably-loud music too. And as you stated, DAC hard clipping in loud material may be less noticeable than with softer material. In other words, hard clipping may get more noticed with softer material.
So this is an additional argument to handle inter-sample hard clipping in DAC designs.
Also, loudness and the amplitude of inter-sample levels aren’t necessarily related; there’s plenty of ‘reasonably-loud’ material showing +2/3dB inter-sample values. High inter-sample values are more connected to high high-frequency transients — which loud music may have, but so does reasonably-loud music too. And as you stated, DAC hard clipping in loud material may be less noticeable than with softer material. In other words, hard clipping may get more noticed with softer material.
So this is an additional argument to handle inter-sample hard clipping in DAC designs.