The law system was probably implemented after Frog saved the Queen from Yakra in the original, uniterrupted timeline (what is that called? Keystone-1?).
Keep in mind, while Crono & Co. do change a lot of events, they also jsut act as "witnesses" in a lot of events that would ahve hapenned regardless anyway. One example being the fight with Azala/Black Tyranno. Obviously, Ayla was able to defeat them in the original, uniterrupted timeline without Crono & Co's help.
My point is, I believe that the King, after Frog saved the Queen by himself sand Crono & Co, made the same decision at the same time, that decision being to "make a justice system blah blah".