Going back to save Crono was completely different than going back to save Serge. You see, another dimension wouldn't have been created to save Crono because they had a clone, meaning that they made it seem to their past selves that Crono had infact died putting them on the quest to save him. If they had just snatched him away, then an alternate dimension would be made where the gang knows that Crono didn't die, just disappeared. That was the purpose of them needing a clone. Who knows what would've happened if an alternate pocket dimension was created.
You know, what you said, along with what happened in CC, makes me think. We've been debating for years why the dimensions split, and we also claim there are no paradoxes (besides plotholes) because of our unofficial laws of Chrono time travel. What if dimension splits happen because a paradox none of our laws can solve is created?
Because Kid saved Serge, she didn't need to go save him. This would've been avoided if she put a clone there, but she didn't. So she realized she didn't need to save Serge. But she did. But she won't. But she will. But then she won't etc., causing a loop that can only be solved by severing the worlds.