If your language already uses a Unicode-compatible string type, you should probably use that.
If you are designing a new language, rewriting a language's basic string primitives, or writing an API or application in a language that doesn't have a well-standardized Unicode string type like C or C++, then it is probably better to pick UTF-8; if your app is necessarily single platform and tied to a platform API, choose that API's encoding, but for anything cross platform, the encoding is going to differ between the platforms so choosing UTF-8 and then transcoding at the API boundaries on the different platforms is fine.
By the way, most languages do have the concept of a byte array, and you can provide UTF-8 string operations on top of that; but as I said, in general, you should be using the language's native string type unless you have a very good reason not to.
The original article that we're discussing does mention one of those very good reasons; in Python, it uses an 8-bit Latin-1 encoding if the characters can fit, upgrades to 16-bit UCS-2 if they can fit in that range, and finally upgrades to 32-bit UTF-32 if they don't fit in the UCS-2 range. But that means that if you're appending strings, and one of them contains an emoji (for instance, in a web templating system that encounters an emoji in a comment), that can mean that all of a sudden your string has to grow to four times its original size, which can cause serious problems; so one workaround for that may be to actually write everything out to a UTF-8 encoded string (which in Python can be represented as a byte array) rather than trying to append strings together and hitting that behavior.
Furthermore, several languages already do use UTF-8 as their internal string type; Rust, Go, and Ruby all use UTF-8 as their default or only string type.
And by the way, Rust and Go both use slices to handle the use case you describe; a slice is represented as a pointer to the first byte of interest, and a number representing how many bytes it extends. I don't know about in Go, but in Rust the API guarantees that all string slices created from a string begin and end on proper codepoint boundaries. Go: https://blog.golang.org/slices, Rust: https://doc.rust-lang.org/std/primitive.str.html.