It doesn’t alleviate anxiety so much as distract you from it. Anything can do that, that’s just what a coping mechanism is. For many people, that might be painting, playing video games, exercise, or anything else. It’s just that nicotine is a particularly unhealthy coping mechanism. There are other unhealthy coping mechanisms too—some people gamble, others drink alcohol, and some people stress-eat excessive amounts of junk food.