For complicated problems, you can't just write the language spec. You need to iteratively develop it, which itself requires some intermediate state/language describing what you know so far. That intermediate state being the end programming language in consideration isn't mandatory per se, but iteratively refining, replacing, and reworking solutions using code as a drafting board is very common in the industry. That's doubly true for languages, where the social pressures in how it "feels" or is actually used are paramount. If you move away from iterative coding drafts, you still need some sort of interactive product to work on to actually develop the spec.

Plus, current-gen agents/LLMs can't implement a non-trivial language spec without significant hand-holding.