Tailoring the message to the audience is really a fundamental principle of good communication.

Scientists and academics demand an entirely different level of rigor compared to customers of LLM providers.

Sure, but they went slightly overboard with that headline and they knew it. But oh well, they have a lot of eyes and discussion on their paper so it's a success.

I feel like, if the feedback to your paper is "this is over-done / they claim more than they prove / it's kinda hype-ish" you're going to get less references in future papers.

That would seem to be counter to the "impact" goal for research.

Fair enough, that might be more my personal opinion instead of sound advice for successful research. Also I understand that you have a very limited amount of time to get your research noticed in this topic. Who knows if it's relevant two years down the line.