Does it though? Let's say you use an LLM to write code, do you think it benefits from the fact that the same model is capable of translating corporate messaging into internet slang for marketing?

I would assume a smaller model trained specifically to produce code based on natural language input would perform at least just as well, which would already be better given the smaller size / probably lower training resource requirements. This is of course, as already said, an assumption. But generalizing typically comes at a cost, there is no reason why this wouldn't apply to LLMs, it even applies to humans.