The main objection I used to have was there are infinite things to do when building a programming language, it's already enough to build 1 compiler, you probably shouldn't also build a second as your main stress test of the language.

That said if your languages is for building compilers you'd probably want to do it. Otherwise, basically no one writes compilers, and if they are they're writing them for their own languages in something much more mature than your nascent language. And if the ambient advice is to bootstrap asap, they'll only be using your language for a hot second anyway, so they're the worst users to cater towards.

These days I think all languages should try to do it with an LLM because, why not? That also means bootstrapping a compiler isn't exactly an impressive feat anymore, most new languages are doing it now.