> The String type _is_ a newtype that […]

It is not. `NonZeroUsize` is (though in Rust "newtype" is only a pattern or idiom), and its definition (inside of a macro which provides numeric newtypes a bunch of `impl`s) is:

    pub struct NonZeroUsize(usize);

But here's String:

    pub struct String {
        vec: Vec<u8>,
    }

…which is a normal `struct` _containing_ a named `Vec<u8>`. Of the types you mentioned, only `NonZeroUsize` conforms to the pattern.