This isn't exactly a new problem we do it with any bit of new software/hardware, not just LLMs. We check its work when it's new, and then tend to trust it over time as it proves itself.
But it seems to be hitting us worse with LLMs, as they are less consistent than previous software. And LLM hallucinations are partially dangerous, because they are often plausible enough to pass the sniff test. We just aren't used to handling something this unpredictable.