You can see instances of this with Minerva, where the finetuned 540b version beats the finetuned 62b version despite being finetuned on only a quarter of the data the 62b version was finetuned on.
The large pretrained model is a prereq for domain-specific models.
Furthermore, when making task-specific models, an 'encoder' architecture (similar to BERT) often works better than a 'decoder' architecture (similar to GPTx), so you might want to use a similar-but-different architecture than the general model intended to be conversational/generative.
Try to start with a NN and 50 images of dogs and cats, and it won't work very well.
For example, if you want a domain-specific model for the legal domain, then you can pre-train a large self-supervised model on every single legal-related document in the world you can get your hands on, instead of a general mix of news and fiction and blogs and everything else - and that might be a more efficient starting point for however many(few) annotated examples you have for your task-specific classifier than the general model.
OpenAI offers the ability to fine-tune some of their models: https://platform.openai.com/docs/guides/fine-tuning
There are also other services that will fine-tune an LLM, for a specific domain, for you: https://activechat.ai/build-your-own-chatgpt/