Malbim says on Esther 8:5 that Esther first tried to get the original decree canceled.
יכתב להשיב – עתה פרטה עצתה הנ״ל בפרטות שישלח המלך רצים לקחת את הספרים
החתומים שבהם כתוב מחשבת המן בחזרה, כי השרים אין יודעים עדיין מה כתוב
בהן, ולא יהיה בזה בזיון אל המלך.
Write to return - ... The king should send runners to take the signed
decrees that had the ideas of Haman and return them, since the
officers did not yet know what was in them, and thus it would not be a
disgrace to the king.
This was impossible to do as Rashi says on Esther 8:8
cannot be rescinded: It is not fitting to rescind it and to invalidate
the king’s writ.
Mordechai could not allow the Jews to attack enemies earlier because anyone that he attacked could claim to have nothing like that in mind. Only Haman could be killed at once because that was a decree of the king. Mordechai was forbidden by Persian law to cancel the original decree. As a result, the Jews were given permission to destroy only those who attacked them on the day that the original decree allowed. Since Mordechai could not cancel the original decree, the enemies of the Jews still had permission to attack the next Adar on the given day. The new decree could only allow the Jews to fight on that day and allowed allies as well to fight on that day. Anyone trying to fight on any other day would be considered a rebel against Achashveros and killed by the king's soldiers.
An analogy would be the pogroms in Russia under the Tsar or the riots in Baltimore we recently had where the police were ordered to stand down and give the rioters free reign. Once the rulers decided enough was enough, the police were freed to stop the attacks.
Esther asked that the original decree be rescinded and Achashveros said that not even he could do that.
And she said, "If it please the king, and if I have found favor before
him, and the matter is proper before the king, and I am good in his
sight, let it be written to rescind the letters, the device of Haman
the son of Hammedatha, the Agagite, which he wrote to destroy the Jews
who are in all the king's provinces.
And you-write about the Jews as you see fit, in the name of the king,
and seal [it] with the king's ring, for a writ that is written in the
name of the king and sealed with the king's ring cannot be rescinded."
Since anything sealed with the king's ring could never be rescinded, they could not even write to punish the enemies of the Jews, since the original decree allowed them to attack freely. Mordechai had to write the new decree carefully to allow the Jews to fight and to avoid giving the enemies free reign to take vengeance on the Jews when the original decree took effect. As a result, Mordechai could only allow the Jews and their allies to fight back.