I find where the argument gets lost is when undefined behavior is assumed to be exactly that, an invariant.

That is to say, I find "could not happen" the most bizarre reading to make when optimizing around undefined behavior "whatever the machine does" makes sense, as does "we don't know". But "could not happen???" if it could not happen the spec would have said "could not happen" instead the spec does not know what will happen and so punts on the outcome, knowing full well that it will happen all the time.

The problem is that there is no optimization to make around "whatever the hardware does" or "we have no clue" so the incentive is to choose the worst possible reading "undefined behavior is incorrect code and therefore a correct program will never have it".

Some behaviors are left unspecified instead of undefined, which allows each implementation to choose whatever behavior is convenient, such as, as you put it, whatever the hardware does. IIRC this is the case in C for modulo with both negative operands.

I would imagine that the standard writers choose one or the other depending on whether the behavior is useful for optimizations. There's also the matter that if a behavior is currently undefined, it's easy to later on make it unspecified or specified, while if a behavior is unspecified it's more difficult to make it undefined, because you don't know how much code is depending on that behavior.