> There are a lot of operations that are valid and well-defined on binary strings, such as (...), and so on.
Every single thing you listed here is supported by &[u8] type. That's the point: if you want to operate on data without assuming it's valid UTF-8, you just use &[u8] (or allocating Vec<u8>), and the standard library offers what you'd typically want, except of the functions that assume that the string is valid UTF-8 (like e.g. iterating over code points). If you want that, you need to convert your &[u8] to &str, and the process of conversion forces you to check for conversion errors.
Every single thing you listed here is supported by &[u8] type. That's the point: if you want to operate on data without assuming it's valid UTF-8, you just use &[u8] (or allocating Vec<u8>), and the standard library offers what you'd typically want, except of the functions that assume that the string is valid UTF-8 (like e.g. iterating over code points). If you want that, you need to convert your &[u8] to &str, and the process of conversion forces you to check for conversion errors.