Actually (at the risk of putting the cat amongst the pigeons) I can suggest a simple experiment people can do themselves to illustrate this in action in the most graphic way, which should dispel any lingering doubt that it's important.
The aim is to show that what looks like a legal 'signal' way below any red light in your system can still represent something that cannot pass even remotely correctly out of your digital mixer at full level. And also to illustrate how this may affect your sound quality in practice when mixing ITB. It's a kind of worst case scenario - but it illustrates the problem.
You need a W/S like ProTools, a signal generator plug-in that has a good filter section that actually goes flat to 20KHz and rolls off at 24dB/oct or so.
- In Pro tools get a mono channel up,
- stick the PT generator plug-in at the beginning of the channel and set it for sine at say 1-2KHz.
- Follow this with a good filter plug-in set for the max slope at 20KHz. (For example the Oxford EQ plug-in has 36dB/oct at 20KHz and illustrates this well - any other good HF filter should work as well).
- As an initial test set the channel fader at 0dB and note that the PT meters shows the sinewave signal at -6dBr and that putting the filter plug-in in and out using bypass has no effect.
- OK now switch the signal genny to white noise and note that the level on PT is still -6dBr.
- Now un-bypass the filter plug-in and watch the signal level rise dramatically!! In the case of the Oxford 36dB/oct filter the meter level will rise a full 5dBr to nearly flat out.
Ok so what's happening - how is this possible? Well the digital genny plug-in produces sinewaves correctly - but when in noise setting it is just a random number generator driving the output. So although when set to -6dB peak value no sample ever gets to be greater than 50% modulation - a reconstruction of the undecoded SAMPLE VALUES produces nearly full level SIGNAL. Reconstruction means filtering and so the filter plug-in is acting like a partial reconstruction filter (much like a DAC) - which in turn is now feeding a more legitimate SIGNAL which the sample value only meter can read more correctly.
Ok now if this SAMPLE train is passing out of your DAC it too is being reconstructed correctly - so this -6dBr noise from the genny would a produce nearly full modulation SIGNAL if you fed this to the DAC directly - even though no sample gets to be bigger than 50% and no reading say's it's bigger than -6dBr.
If your filter is a good one you should be able to switch it in and out and hear no difference in the sound of the signal from your DAC - despite the PT meter reading wildly different. The filter has neither added nor taken anything significant out of the intended audio signal - but you have nearly doubled the sample values within the PT channel!
Ok, now wind the genny level up to say -2 or -3dB (still less than only 75% full level) and do the same thing. What happens? Well it now clips when the filter is in (samples bigger than flat out) - now the sound definitely changes when you switch the filter in and out - because it is mathematically limited and in error when the filter is in - cos it cannot pass through TDM slot at the output of the filter!!
That is what would be happening in your DAC, it would saturate if you sent this at only 3dB setting on the genny - reading -3dBr within the mixer itself, straight to the output!!
Ok now what does this mean for a mix? Well with all those mixed signals, cymbal crashes, HF EQ and limiting etc.. how close do you imagine the output signal can get to being a bit like white noise in places within a real production - even if none of the contributing channels hit the red light? Is this not the exact register of what we term as 'air' and 'resolution'? And people are aiming at max possible mix output levels on meters that do not show SIGNAL.
So why does an OTB mixer apparently sound better than an ITB mixer when you are modulating your digits close to 0dBr (sample value) all over the place? Well all those DACs (flawed as they may be) are acting to legitimately reconstruct your programme - before - you mix them all together and produce too many illegal signals that cannot pass out of your digital mixer! Paradoxically, the loss of sound quality due to all those converters is not as bad as the illegal signals created within the digital mixer by the 'too hot' signals you are trying in vain to pass out of the system.
It is not a summing issue at all (the one thing digits CAN do is add up almost perfectly). It's an illegal output problem caused by the fact that there are no meters that display actual SIGNAL in your whole mixing environment - you simply never see it happening.
So - go back and get your fav test mix back up on your W/S, re-mix the whole thing making sure that at every place in all chains (including between all plug-ins) never gets bigger than -6dBr. Make sure your final output after any limiting etc also never peaks beyond -6dBr. Now do the comparison between this ITB mix and a similar OTB mix. You might have a big surprise