This was originally posted on GameFAQs.
It is possible to defeat Lavos anytime after the travelers reach the End of Time, but this is not reasonable in the context of the story. The purpose of the time travelers' journey is to gain the power to defeat Lavos. Gaspar says that the travelers will die if they enter the bucket, which is true. After the Ocean Palace disaster, Gaspar lists even more tasks the travelers must complete to ready themselves. The existence of the bucket-portal is one of the items which gives the player remarkable freedom in an otherwise linear game.
The planet is dying, and it is reliving its experiences--the history of the world--through the actions of the time travelers. The inhabitants of the world do not need saving. The intervention of the Entity did not change the outcome of history: the humans prevailed over the Reptites due to the ice age. Zeal was destroyed by Lavos, and Guardia defeated the Mystics. Only in the future when the time travelers saved the remaining humans from genocide did they have an effect on events, but this time-line was destroyed when Lavos was defeated.
The Entity did not create the Time-Gates to change history. The planet is using the events of its past to shape the character of time travelers, to give them the power to defeat Lavos and more importantly show them why they should fight. The results of the time travelers' actions are directed inwards, to empower themselves. The only lasting changes to the time-line are events which affect the travelers personally. Ayla gained an insight about the Reptites' nature. Magus achieved his revenge. Frog restored his honor. Marle reconciled with her father. Lucca resolved her purpose in life. Robo learned to experience human emotion. And, if I may project my own feelings onto Crono's character, his reason to fight was his companions, who were the driving force for his every action in the game.
Chrono Cross is exactly the same. Schala is imprisoned by the Time Devourer in the Darkness Beyond Time. The Entity is indifferent to the eventual destruction of the universe because the TD is completely beyond the scope of the planet. Only Balthazar had the power to act, and his only goal was to rescue Schala and prevent the destruction of the universe. The sole purpose of Chrono Cross was to combine Serge with the Chrono Cross to defeat the Time Devourer. All of Serge's actions leading up to the final battle are irrelevant because they are undone upon the completion of his mission. These events serve only to empower Serge who, as the arbiter of time, is the only person capable of defeating the Time Devourer. I think the Time Crash and the following events actually had an overall negative effect on the time-line. Serge's actions ultimately benefit himself and not the people he is trying to protect.