> IFNDR is a catastrophe because it truly does render the entire software without meaning.

In the language. I.e. the language assigns no meaning to source the program, which is, indeed, the "catastrophic" impact of UB (or IFNDR) within the theory of the language. But since a running program takes the form of an executable, and the executable always has a defined meaning in another language (machine code), while C++ has nothing to say about what such programs do (i.e. that's the end of the helpfulness of that theory) that doesn't mean we can't talk about or care about the meaning of the executable.

An executable that crashes and an executable that leaks all your secrets have very different consequences, and while the C++ spec says absolutely nothing about the relationship between different UBs and these behaviours, that doesn't mean that these relationships don't exist.

A mathematical singularity in a physical theory means that that particular theory has nothing to say about the physics of that situation, not that there's no actual physics going on, and the physics that is actually going on could be more or less "catastrophic" depending on what we mean by that.