That is a very limited way of thinking. A missile is not an 'at will' weapon. Am not talking about you being able to fire the missile any time you like. Am talking about fielding a weapon that you can fire at will, recall it at will, and fire it off again at will. A ship, a tank, a platoon of soldiers, or an aircraft are all 'at will' weapon. You can fire them off, issue them new orders, hold them in a pattern, and eventually recall them home to make them better. You cannot do that with a missile, which is essentially a throwaway weapon.
An aircraft carrier give you the most flexibility in terms of having an immediate offense and/or a threat in holding. In any area where the carrier's primary weapon, its air wings, can reach, you have an area of influence that will compel others to adjust their positions to accommodate your presence, and if they are in the inferior, their readjustments will make you the superior without you doing anything other than to be in the area. You cannot have that kind of influence with an arsenal of throwaway weapons back in the homeland.
Your line of thinking is nothing new. They predicted the demise of navies, not just of large ships but about entire navies, after Mitchell demonstrated ships can be bombed from aircrafts. Yet for today, navies are just as relevant to warfare and diplomacy as ever. Objectively speaking, if China does not make this effort even with a 'training' carrier, it will go down in military history as one of China's greatest mistakes.
