One of the most frustrating parts of rust (for me), is that `std::cmp::min` (and some other methods) require that their arguments are `Ord` (totally ordered), and floats are only partially order because of NaN, so you can't use std::cmp::min on floats.
I do believe that's quite intentional, due to the inexactness of floating-point values, it's not "right" to do that. There should be a `partial_min` function though, IMO, which has weaker guarantees.
Safety is the whole idea behind Rust, and if you draw the line here, that's neither in line with the Rust ethos, nor particularly valuable. After all, code that "expects to handle" null was pretty rare too ;)
Safety in Rust's context is UB-free, memory errors-free, data race-free.
Safety in software engineering is more about designing systems with some degree of assurance against certain failures, but not about surprises or expectations of a programmer.
The usage you call traditional is perhaps common, but not really rooted in anything in software engineering. I'd call it an informal meaning, maybe.