What benefit is gained from making your new language's compiler self-hosting? To me, it seems this only adds complexity to your build. If it can generate code for your language, why does it matter what it's written in?

I understand that a compiler is a good proof-of-concept program. They're generally dependency-free and will put your language through its paces. The exercise of writing a compiler in your new language is a good idea, I'm not arguing that point. I'm less clear on why making that self-hosted compiler the canonical version of your language is beneficial. Wouldn't keeping your compiler written in something like Haskell or OCaml make it more extensible and flexible, and quicker to build?