I do think there's a similarity in how creative you need to be though. It means that applying LLMs to new problems isn't as straight-forward as people make it seem at first, and isn't necessarily reliable. In contrast, labelling data is something that has a much smoother effort to reward curve for most problems. The experience of labelling the data, training a model and getting it hosted isn't as seamless as it could be -- we're working on that.
I do think classification is pretty fundamental though. The way I see it is, model outputs can be either human-facing, machine facing, or both. If you're going to feed the output into another system, that system wants the data to obey some limited schema, so that you can run logic based on it. For instance, let's say you want to trigger some alert when a particular kind of article is published or a particular kind of message is sent. Triggering the alert is a boolean thing, so that has to be a classification task. You might want to also attach text in the alert, so that's a human-facing part.
I agree that there's lots of ways that LLMs can be used iteratively, allowing more trade-off of computational cost for accuracy. I just think in a lot of cases, the best way to exploit that is to trade towards as much accuracy as you can get, and use that to create training samples. You can then manually correct the training samples as well --- if they're mostly correct, reviewing them is pretty quick. You can then train and evaluate a smaller model.