They're not math errors, it's the most sensible thing to do: when you overload a speaker, you get clipping, not some weird thing where the cone snaps to the opposite side of the range.
I’m talking about the basis of the analogy, not the analogy. If you’re processing audio signals, saturation (i.e. clipping) is of course preferable to the alternative.
“Destructive”, regardless how minor, should be intentional or at the very least conscious. This is one of the various reasons why serious audio processing is done as 32 bit float: no (practical) risk of unexpected overflows.
