I suppose that's a fair point. I guess a better analogy might be to operations on normal integer types, where overflow is considered an error but that is not reflected in default operator function signatures.
I do want to circle back a bit and say that my mention of signaling NaNs would probably have been better served by a discussion of floating point exceptions more generally. In particular, I feel like existing IEEE floating point technically supports something like what you propose via hardware floating point exceptions and/or sNaNs, but I don't know how well those capabilities are actually supported (e.g., from what I remember the C++ interface for dealing with that kind of thing was clunky at best). I want to say that lifting those semantics into programming languages might interfere with normally desirable optimizations as well (e.g., effectively adding a branch after floating point operations might interfere with vectorization), though I suppose Rust could always pull what it did with integer overflow and turn off checks in release mode, as much as I dislike that decision.