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But if you started a spinning top in the middle of a circle, and it wobbled to the left, it wouldn't then automatically come back to the centre each time

I agree you can shoot tighter groups at distance due to things that have no correlation to ballistics, e.g scope parallax, shooting style, eye sight, target size. Not a bullet suddenly correcting...

I'm a strong believer of groups not tightening up at longer range. In practice you might see it but over a large average it's not possible. Unless someone can show me actual scientific reasoning how...

Bullets don't get more stable... they are spinning as fast as they are going to spin when they leave the barrel