Why was Excalibur not used near the end of season 2?
In SAO Wikia about Excalibur, there is some trivia mentioned, among which:


  Kazuto resolved to never use Excalibur for personal gain as he believed that the sword contained the «caliber» of himself and his companions.




As mentioned in the comments and in Alchemist's answer, Kirito used the sword when fighting off the guild to buy Asuna some time.