One person's social anxiety is not another person's social anxiety. I think this is like asking if it's possible to become a professional athlete. It's possible, but not everyone who wants to become a pro athlete becomes a pro athlete.
Everyone is subject to different conditions. Some people face fewer obstacles, or have more support, or have a different temperament, or stumble across a particular technique that works for them. I don't think we should dismiss the claims of people who say they have overcome their social anxiety, or argue that they 'never really had' social anxiety as some people do. Humans are complex; we experience anxiety only when certain thresholds have been met, which depend on conditions which may be altered; and neuroplasticity suggests that real changes are possible. So I don't think it's irrational to hope that we may be able to reduce our own anxiety to levels where we no longer experience it as an obstacle (ie. that we can feel cured). But I think it's important to be realistic, to acknowledge that it may never happen, and take a long-term approach.
Personally, I don't think curing social anxiety should be the goal anyway. I think people should be focusing on developing strategies that allow them to achieve particular goals essential to their well-being, regardless of whether or not their anxiety ever goes away. You can improve the quality of your life in various ways that don't necessarily demand that you overcome your social anxiety. The goal should be increasing your happiness, not trying to conform to some kind of social norm. And in time, these changes may reduce your anxiety all on their own.
Is it just me or is it getting crazier out there.