You can buy more land based fighters and aerial tankers for the same money, but that doesn't mean equal or more capability. Contesting the first island chain is meaningless if you can't actually take islands into your own control.
The area covered by the first island chain is vast, and its distance from Chinese shores is great. China isn't exactly buried in larger airfields that can act as main operation centers outside its immediate territory.
The first island chain is not that far. Everywhere is within 1000km of Chinese airbases, which is feasible for airborne tankers plus heavyweight fighters (F-15/F-22/Su-27/J-20) to cover.
And we've just seen China build 3 brand new airbases in the middle of the SCS, and which provide permanent presence.
China-Korea is 400km. Taiwan is 200km away. Okinawa is 700km. Philippines is 900km. Malaysia/Brunei/Saigon are 500km
Shanghai to the Japanese Home islands is only 1000km. And in order for fighter jets from a Chinese carrier to be useful in this scenario, it's going to have to sail right off the Japanese coastline. Do you seriously think a Chinese carrier can survive in this scenario?
I'm not saying that China shouldn't build carriers, but there is no point building them unless you plan to use them beyond the range of what land-based aircraft can do.
Carriers are better used in the open ocean where there are no airbases available and where they can use their mobility to hide/strike across great distances
EDIT
That also feeds into why China needs more Type-55, because they are more survivable than a carrier and can rely on land-based air cover to perform sea control within the first island chain.