In my experience LLMs can get about 70-80% accuracy on a bunch of NER and text classification tasks if you give it a reasonable prompt. That's not nothing and it's something that you can get started with super quickly. But you'll have slow responses and typically a 3rd party running the inference.
Annotating data yourself to about 2000-3000 examples, on the datasets that I ran my benchmarks on, may get you closer to 80-90%. You'll typically also get fast inference that you can run on your own hardware no problem. By annotating the data myself I also like to think that I understand the problem much better as a consequence.
Don't get me wrong. LLMs are cool and interesting ... but they don't seem to replace old-school methods just yet.