Until recently, carriers were apparently able to avoid missile hits simply by moving at full speed - I guess it's still not trivial for a ballistic missile to hit fast, mobile targets (the US missile defense program probably faces similar engineering issues). The Chinese recently shifted the balance of power in the Pacific theater by developing a missile theoretically capable of taking down US carriers from afar. http://www.ft.com/cms/s/0/3e69c85a-1264-11e0-b4c8-00144feabd...

Regarding whether or not this is a practical asset, so much of military power is "soft" (you might say political, but I think that's an oversimplification), I don't think you could fairly call this an impractical asset. China has traditionally focused on maintaining power in there sphere of the world. As others have noted, the power of an aircraft carrier is that it allows you to project power globally. They could send the aircraft carrier to a lot of places that would make other countries unhappy, but not unhappy enough to actually start a military attack over it - thus the carrier would have been an effective tool.

From a more political perspective, there's been a regional arms buildup. India already has a carrier and is building more, and India and some other Asian countries have been buying up submarines.