What if the initial training already contains all necessary data for a particular specialization? What would be the benefit of continuing the training process?
Imagine someone tells you about how someone committed a crime and asks you to summarise. Now imagine the same question is asked to a lawyer. Even if you both knew the same facts, the response would be very different in style, highlighted points, mentioned references, etc. The domain specific fine tuning does exactly that. Sure, sometimes you can get very close by changing the prompt to include "respond like a lawyer in situation X with following extra rules", but not always and the fine-tuning gives better results and shorter prompt.