1. I'm not sure I'd say "broken". The problem is, what is "insufficient headroom"? Typically about 3dB should be enough but that would still leave a small percentage of commercial audio clipped.
"Broken" = "insufficient." Different terminology describing
design deficiency. In a properly designed audio chain (Analog => ADC => processing => DAC => amp) signal integrity is maintained, and sufficient headroom is designed-in. If the original analog signal is not clipped, and the ADC properly converts the signal, the resultant PCM data will be unclipped 100% of the time. Yes, PCM processing (DAW, plugins, etc.) can screw anything up via user error, or poor design, or not having proper metering to assess PCM clipping. That's poor design or operator error, and has nothing to do with "headroom above 0dBFS." In PCM, there is no such thing as "headroom above 0dBFS." Any attempted signal above
true 0dBFS in an ADC or DAC is a clip, therefore "undefined" or "invalid" in Nyquist space (caveat: if the ADC or DAC designer arbitrarily set 0dBFS at some level below true rail-rail (Vpp) clipping, then yes, there could be "headroom above 0dBFS" -- which is actually a common design technique, more about the historical migration from analog to digital signal paths than an objective design requirement). If an operator has maintained unclipped program through the processing stage, then a properly designed DAC will maintain unclipped data back to analog, 100% of the time. Inter-sample clipping is a result of poor product design and/or operator misuse.
your statement is pretty much irrelevant as there is almost no commercial audio content available which hasn't been mixed and therefore an "original signal" is not what gets distributed to consumers.
My statement is entirely relevant throughout the entire audio sampling and processing chain (see above). A properly designed digital mixing engine, or any digital processing system, will maintain unclipped signal integrity unless the operator pushes the program level beyond full-scale. In a properly designed digital metering system,
all peaks are identified. In a poorly designed digital metering system, some peaks are missed, which is missed inter-sample information. Poorly designed tools, nothing more. We also know that most mixing engines are based on a 32-bit IEEE float topology, which assures that all 24 audio audio bits are maintained perfectly (the actual mixing algorithm is a different story, which is why different DAWs sound different after a mix), hence any "missed clipping" after mixing results from either insufficient tools or operator error.