kwaigonegin
Colonel
Nuclear reactor for the submarine is quite different to nuclear reactor for an aircraft carrier.
Its one thing to build a nuclear attack or ballistic submarine, but completely another thing to build a nuclear aircraft carrier.
The safety measures and various subsystems that goes into it in order to protect it from disaster is far more complex than a submarine - for a nuclear submarine to go horribly wrong you lost 150 people, but for a nuclear super aircraft carrier to go horribly wrong that will be 5000 dead people, plus all the investments that goes into building a huge aircraft carrier, ALL the aircrafts and helicopters that are onboard, all the weapons, stores and ammos, not to mention the cost of training 5000+ personnels to operate an aircraft carrier. It is just far too costly if something goes wrong, so that's why most of the country that dares to invest in a nuclear aircraft carrier takes decades in design and testing it.
That's why for all the countries that has developed the nuclear submarines, ONLY TWO COUNTRIES actually dares to put into production nuclear aircraft carriers - the french and the american. Not even the british and the russian try it - the latest Queen Elizabeth-class aircraft carrier is conventional, and there are no country that are planning for nuclear aircraft carrier in the foreseeable future.
It will take SEVERAL DECADES before China will embark on nuclear aircraft carrier, that is if they go the completely indigenous route. They get it sooner if they can get the french onboard to help them, but it is highly unlikely.
Also, let's not forget, why would China want a nuclear powered aircraft carrier? Are they planning to be the new global police? A nuclear powered aircraft carrier goes against the current (and even the near future) chinese strategy. China is only seeking to consolidate its near shore defence - maybe along the second island chain, and the aircraft carriers they planning to build are only going to run around these areas most of the time. The PLAN aren't going to send their precious aircraft carriers too far from their shore, at least not until they have enough number of them. So a steam-powered gas turbined aircraft carrier is more than enough to fit the PLAN strategy for the foreseeable future.
Believe it or not it's actually harder to put a nuke plant inside a boomer or fast boat than it is on a suface ship. I believe the primary issue for PLAN's reactors is not so much of installation but rather power generation.
To power a carrier you need exponentially more power generation than you do a sub and at this point I do not believe China has the tech that is mature enough and small enough to fit multiple reactors inside the hull of a 70K carrier that would compromise other functionalities of a carrier.
Another reason would be simply strategic like you said. You don't need CVNs if you do not intend to travel the world's oceans. If you don't often sailed more than a thousand miles off your coastline or home port a CV is probably much preferred.
China also do not currently have large enough overseas naval bases nor forward deployed CSG and probably won't in the near future.
Until PLAN has true naval bases in the Indian ocean, Atlantic, Med etc a CVN is probably not the top priority. I would say at least another 10 yrs before they have a CVN but it's more to do with because they can and not because they really need it from a benefits perpective.