This is a variation on the old Grandfather Paradox. The Weyrleaders in Moretas time are perfectly aware of the dangers of doing so. In "Moreta" Leri and Moreta treat it as essentially classified information with severe penalties for riders who use it irresponsibly. I can hypothesize that bad things often happen when the ability is used. I would use as an example the change in Kylara when Ramoths first hatching weyrlings are sent via timing to Southern Weyr to mature. I would also cite the inability of the initial Southern Weyr riders and weyrfolk to tolerate being in two different times simultaneously, etc. Recall also just before the start of the 9'th pass when Lessa inadvertently visited Ruatha of the past. That visit saved Lessa but also allowed Fax's invasion to go unchallenged until too late when the Watchwher failed to give alarm because of the presence of Lessa and Ramoth in the sky.
Finally I think I can defer to Masterwordsmith McCaffrey herself. When Lessa returned from bringing the old-timers forward and made an initial overshoot because of the severe effects timing has on dragon and rider Lytol gave her directions to get back to the proper time. Although not stated directly- the verbiage used implies that you cannot go back and change the past- because you didn't.
i recognize this is an old post but the topic is an interesting one.