I believe the AK4493 places the digital volume control in front of the interpolator.
FWIW, I've been testing at zero attenuation from the internal volume control.
Take a pure 1kHz sine. At +3dB overload, the waveform and samples look like this:
It's very audible.
+3dB overload on complex music you likely won't hear. I've got DAC overload test CD tracks (music) where +9dB is audible, but certainly not unlistenable.
You are not showing intersample-overs here. You show digital hardclipping in the original sample rate.
There will be a tiny amount of intersample overs at the edges in this example waveform
BTW, Audacity cannot show how the reconstructed waveform would (approximately) look like. You have to upsample it yourself.
As you know, the fix for this is not free. We lose dynamic range for all content and all times. The real solution would be to avoid this in production of the music, not consumption. Or use DSP volume control upstream of the DAC.
I'm all for expanding testing where it is important, but this is a non-issue and is solely caused by the content being poorly recorded in the first place. It's not up to D/A converters to "fix" mastering issues, especially at the expense of ultimate performance. What's next? 6/9/12dB headroom? Should the D/A converters fix channel imbalances too?
I'm of the opinion that a DAC should be signal-agnostic and make no assumption if the inputs stream is "ill-formed" or not. Actually it is the reconstruction filter of the DAC which creates the IS-Overs in the first place, therefore it is the place where it should be handled.
It should take care of the issue in a sane way, which would be to provide some headroom for IS-overs like +2...3dBFS and apply gentle softclipping starting at +1dBFS. Internal headroom (before the softclipper) should be +10dBFS. At any rate, broken output signals should be avoided (no funny stuff like wraparound and always keeping the DS modulator in a safe, non-overdriven state).
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As for the testing, I think the truly relevant region for application is the -10 to -30dBFS region (well, right were the ESS hump happens to be). 0dBFS of course must be handled flawlessly but a certain rise of distortion is irrelevant. In other words, a DAC that is worse at 0dBFS than another might still be much better in the relevant region.
And IS-Overs up to a certain reasonable level, say +6dBFS, should be handled gracefully, that is, provide signal fidelity up to about +1dBFS and then start a gentle soft-clipping maxing out at +3dBFS not matter how high the true peak would be. And this should be tested at the most brickwall'ish filter setting as that is the most prone to produce the largest IS-Overs.
And I think the problem is much more relevant in ASRC chips and DSP processing in general because that may corrupt a signal that is reused/recorded etc.