Why though? China's building drone carriers instead. Taking down aircraft carriers is of course no simple matter, but hardly infeasible for a super power. The problem with capital ships is that they're just as expensive to replace as they are to build. Also, blowing one up eliminates 9% of the US' AC fleet at a stroke, which would be a big psychological blow. I don't think China is as emotionally invested in its aircraft carriers and built them primarily to show that they could. That said, in any military conflict with China an opponent would be well advised to target their nearest aircraft carrier as early and powerfully as possible for the humiliation factor.