Base models have a lot of capabilities - arranged in all the wrong ways for high performance reasoning and problem-solving. The power of fine tuning on "a couple thousand of input-output pairings" is that it can fix some of that. If your pairings are very well chosen, that is.
Why? They often don't make sense. They send DMCA takedowns over materials they can't even copyright, for example. They fessed up to creating shadow libraries that they didn't even use in their training corpus, resulting in the largest copyright settlement ever. Your reasoning is flawed.
Base models have a lot of capabilities - arranged in all the wrong ways for high performance reasoning and problem-solving. The power of fine tuning on "a couple thousand of input-output pairings" is that it can fix some of that. If your pairings are very well chosen, that is.