I think Xander's ability to "see" accumulated gradually over the course of the series. In season one, his thinking was very narrow. His lines were often dominated by black-or-white thinking. "I don't like vampires. I'm gonna take a stand and say they're not good," he said in WTTH after vamps got his friend Jessie. By Prophecy Girl, his thoughts were still pretty much the same. "I don't like you. At the end of the day, I pretty much think you're a vampire," he told Angel. Good was good and bad was bad and Xander was not able to see very much beyond that. Even so, there was a small germ of potential there. Faced with Buffy's dead body, Angel was quick to give up hope. Xander saw more possibilities, one of which ended up saving Buffy's life. This starts a trend. When all hope seems lost, Xander is often the one to see a new and better way to bring the situation to a favorable resolution.
While I agree that this trait is amplified in season 7, I don't agree that it's just a season 7 thing. Xander was flawed and he made a lot of mistakes over the years, yes, but his emotional connections to the other characters did often allow him to see the solution to problems. At the end of the day, he had a lot of valuable insight into others' emotions. He was able to see little things, like the fact that Cordy needed a new dress in season 3, as well as bigger things, like how to reach Willow in season 6. By season 7, Xander had matured to the point that he was able to apply that gradually acquired skill in order to finally work with a vampire, to guide and assist the potential slayers, to be a much-needed male role model for Dawn, etc. So while I certainly agree that this was certainly more noticeable in season 7, I can't say that it was strictly a season 7 trait. I think it was a Xander trait that, like Buffy's leadership skills and Willow's self-confidence, was amplified in the last season as we went hurtling toward a finale.