I am going to have to agree that the court system was there even without Crono's involvement. Leene obviously was saved in the original timeline, so it can be assumed that the Chancellor was saved also. I couldn't fathom why Crono Frog and Lucca saving them would have any effect on the Chancellors decision to make a court system to do away with fiends like Yakra.
What changed in the new time-line was that Yarka's descendants wanted revenge on Crono, Marle, and Lucca for interfering in the past.
