Some systems saturate/overload/soft clip (could be tape, vinyl, amplifiers) causing added distortion.
Just a FWIW, obviously you have not spent any time around an LP mastering system. They can't be overloaded, in fact the LP cutting system is the most dynamic audio process in existence, as far as I can tell. The amps typically have 10X more than what is demanded of them, and the cutterhead can cut grooves without distortion that no stylus/arm combination could hope to track. In short, and LP cuttersystem can't be overloaded. The limit is in the playback but more so with the final product rather than the lacquers. There have been recent advances in pressing operations that have eliminated most of that too- so the LP now is capable of dynamic range that rivals that of digital. It is different from tape in that regard!
It goes on all the time in audio.(a) Do you think that this effect can be a useful substitute for extra dynamic range?
(b) Do you think that these systems may have been designed, or may have evolved, in the way they have, because of this characteristic?
I think SET amplifiers are the best example of this. Universally with all SETs you will see that they are perceived to have much more 'dynamics' than their low output power would suggest. This is caused by the distortion character of the amplifier.
(e) Would you rather have a system that was 'saturation'-free up to any volume you wanted, or one that had the characteristics of existing vinyl/tube equipment?
Existing vinyl/tube equipment can be quite 'saturation'-free up to nearly any volume you want already.