The game ends when the Millenial Fair. Any kind of intervention with Crono's jouney in 1000 A.D. could mess up the future. Therefore, once the Millenial Fair ends, the future is secure. The Midnight Parade is the one point in the story in the Millenial Fair when everything's already pretty much in order. So, until 1000 A.D.'s Millenial Fair is over, no one could go. Because any intervention with Truce's past at any point and until the end of the Millenial Fair could somehow stop Crono from saving the future.