Maybe I forgot something because I haven't played the game in a while, but how do we know there is a timeline where Crono never time traveled?
It's a presumption we make about the game that there is a timeline that they don't time travel in because Lavos destroys the future (suggesting he did so unopposed) and also from the ending of the game where Lucca is sad because Robo is returning to a future he won't/doesn't have a place in because the future was changed.
However, just as their are several "what if" time lines in the Chronoverse, who's to say the there isn't a timeline that has an approach similar to the time traveling episode from Gargoyles (or at least one in particular I'm thinking of) where the events portrayed in time itself already include what would've happened from the time travel. In applying that to Crono trigger that would mean that despite Crono and teams' efforts, the future they see is the future this is still going to be, and Lavos still destroys the future anyway. Granted, the game doesn't take that approach because the characters can and do change events in the timeline.
