No, I do not believe I made false equivalency there. Nuclear propulsion being "viable" for aircraft carriers has only been an assumption, and even if such assumption held that does not translate to being advantageous. US GAO's 1994 report comparing conventional vs. nuclear carrier concluded that nuclear carriers cost more yet don't do anything that conventional carriers can't do.
The false equivalency exists in the sense that CVNs, SSNs and SSBNs continue to exist in service in the world's preeminent navy while past nuclear surface combatants no longer are.
From memory, the GAO outcome was that CVNs have higher life cycle costs than CVs and have higher maintenance requirements than CVs, but CVNs can sustain longer distance transits at higher speeds than CVs, with better acceleration, and transit indefinitely without having to replenish its own propulsion fuel, but all else is held equal assuming the CVN and CV alternative designs are equal.
There are also certain factors that the GAO looked at which are not quite as material to the PLAN, such as USN operating their carriers in relatively permissive environments even say, in the Gulf War, as well as having a larger refuelling fleet that was able to be comprehensively operated and defended with minimal risk of targeting which the PLAN may not have the benefit of in a high end conflict.
This has also been covered by GAO's report. Most of the fuel consumption in a task force comes from escorts, not the carrier, as the carrier has higher fuel capacity and is more fuel efficent. Conventional carriers can go ten days before having fuel drop to 30%, a level when refueling becomes mandatory. Operationally, there was no difference in replenishment frequency, as conventional and nuclear carriers both underwent replenishment every 2-3 days.
The elimination of supplying a carrier's own fuel would only bring about a slight benefit, as in it would be noticable only after two weeks of deployment. However, there isn't really a reduced logistical burden, as the burden merely got shifted to shore-based facilities. Benefits that incur penalties elsewhere are not really benefits in my opinion.
Ultimately, China has to build at least one nuclear carrier to run the number themselves. However, the assumption that nuclear propulsion being "viable" for aircraft carrier is just that — an assumption.
Considering the world's leading carrier navy has continued to procure CVNs as its primary carrier force, the term "viable" is pretty reasonable as a baseline to operate from.
It's valid to say that it is yet to be determined if CVNs or CVs or a combination thereof, is "preferred" for the PLAN's future carrier fleet composition, but in the specific case of 004 being built at Dalian we are going based off the same workbook as we always have --- credible rumours, images, and reasoning. And thus far its identity is being pointed much more likely to being a CVN than CV.
As far as eliminating a carrier's own fuel for its onboard propulsion goes -- ideally that can be determined by knowing how frequently AOEs/AORs would be required to sustain maximal endurance patrols in context of HIC settings.
The problem for the PLAN is in a high intensity conflict they'll have to assume their AOEs/AORs are likely going to be high value targets. Even if they have the AOE/AOR hulls to adequately supply a CVN or a CV CSG in peacetime, whether they have sufficient escorts to accompany the replenishment ships and sufficient replenishment ships to enable a CVN or CV to operate at equal cadence/endurance should be the major advantage/disadvantage in carrier propulsion choice.
One of the meaningful differences the GAO report considered was this part comparing a CVN CSG and CV CSG holding as much equal as possible:
"We compared the endurance of a notional conventional carrier battle group to a nuclear carrier battle group using Navy fuel and ordnance consumption rates contained in a 1993 Center for Naval Analyses report.26 The notional battle groups we used consisted of either a conventional or nuclear carrier, plus two Ticonderoga-class Aegis guided missile cruisers (CG-47/52s), two Spruance-class destroyers (DD-963s), and two Arleigh Burke-class Aegis guided missile destroyers (DDG-51s). Each battle group was supported by one Sacramento-class supply ship (AOE-1). We estimated that the conventional battle group would have enough (1) fuel to steam for 29 days, (2) aviation fuel to operate at a tempo comparable to the final days of Desert Storm for 17 days, and (3) aircraft ordnance for 30 days. The conventional escorts of the nuclear carrier battle group would have enough fuel to steam for 34 days, while the nuclear carrier would have enough (1) aviation fuel to operate at a tempo comparable to the final days of Desert Storm for 23 days and (2) ordnance to operate for 41 days."
The CVN CSG had fuel to steam for 34 days vs CV CSG for 29 days, aviation fuel for 23 days vs 17 days, ordnance of 41 days vs 30 days.
How much of that can be accounted for by holding design consistent is a different question (such as ordnance and aviation fuel, as USN CVNs were designed a bit larger than their largest CV counterpart), as we would have to consider whether the PLAN could build a conventionally powered ship with the same footprint as a CVN as well.... in which case the most significant difference would be the "fuel to steam" difference of 34 vs 29 days.
Is that difference of 5 days worthwhile? For a LIC, I would say it probably isn't. For a HIC, I am less sure.
