I think this is conflating two different concepts, only one of which concerns uninhabited types. If the programmer "knows" that a condition is impossible, but can't prove it to the Rust compiler, then they can the `unreachable!` macro to signal their intent to the compiler; in this case the compiler knows that it cannot trust the programmer (because it has no proof) and so generates code anyway that will handle the impossible condition (in this case, by panicking, which is the typical Rust reaction to a signal that the programmer's assumed invariants have been violated).
On the other hand, the use of an uninhabited type means that the programmer has to prove to the compiler that the type is uninhabited, in the same way that declaring a function as returning a String requires the programmer to prove that the function actually does return a String. If we have a function that returns a String, the compiler does not generate any code to handle the case where that function returns an integer instead; that just doesn't make sense, we've used the type system to prove that can't happen. Likewise, it wouldn't make any sense for the compiler to generate code to handle the case where a function returning an uninhabited type returns anything at all.
On the other hand, the use of an uninhabited type means that the programmer has to prove to the compiler that the type is uninhabited, in the same way that declaring a function as returning a String requires the programmer to prove that the function actually does return a String. If we have a function that returns a String, the compiler does not generate any code to handle the case where that function returns an integer instead; that just doesn't make sense, we've used the type system to prove that can't happen. Likewise, it wouldn't make any sense for the compiler to generate code to handle the case where a function returning an uninhabited type returns anything at all.