Yep, BUT:
a) until Taiwan is "neutralised" this way or another, ESF isn't so important
b) what's the easiest way to hurt China ( by the USA, Japan etc. )? Cutting the vital lifeline goeing from the Middle East trough Strait of Malacca to South China Sea. So, in the immediate future ( next 10-20 years, barring any unpredictable changes ) IMHO the most important fleet ( that needs carriers the most ) will be the Southern Fleet, so the carriers will mostly go there.
I don't think there is to be debated on that end. Because realistically, containing China through a trade embargo though it would be an unofficial declaration of war, it doesn't force any potential foe to fire a shot. This is why I never mentioned singapore, it all depends on how their relationship with China grows. even then, its quite hard to think friendlies like Ma and sing would actually directly allow any military to actively sabotage trade with China.
I can concede that realistically, a Stronger South Sea Fleet is the most important naval goal for the PLAN. It reminds me of the pacifc war.
But to actually go further, what about the CPEC? And of course mother russia, could one realistically stifle the PRC engine oil needs?