The lack of oversea naval bases can only be resolved by building oversea naval bases.
The common misconception a lot of people have is that nuclear propulsion gives a ship infinite endurance. What people don't take into account is that the crew still need food and aircraft still needs fuel, so the endurance of the carrier will last until whatever runs out the soonest. Even if we were to assume a nuclear carrier has infinite endurance, the escorts won't.
Both you and Phead are correct -- you are correct in the sense that nuclear propulsion does not provide infinite endurance because a ship always has other consumables and the task force will inevitably have non-nuclear escorts.
However Phead is also correct in the sense that a nuclear powered carrier does still provide benefits to a task force in terms of endurance wholesale. He did not write it himself, so I will write it -- but the fact that a nuclear powered carrier does not need to undergo underway refuelling for its own propulsion/transit needs is a non-trivial advantage, especially in context of sustaining higher speeds.
The benefit for a task force (which is composed of conventionally powered escorts) is the reduced need to refuel the nuclear carrier relative to if it was conventional.
If nuclear propulsion were so great, US and Soviet Union would have went with all-nuclear fleets. And they tried, only to realise how bad of an idea that actually was. The US sticks with nuclear carriers not because nuclear propulsion is wonderful, but because of entrenched interests, essentially suffering from 体制问题 and not something that China should emulate.
A bit of a false equivalency -- nuclear propulsion being viable and sensible for some types of platforms (such as aircraft carriers of certain roles, and SSNs or SSBNs) doesn't mean it is mandatory/desirable/cost-effective for every type of vessel.
I think it is important for people who are supportive of the idea or skeptical of the idea, of a nuclear powered supercarrier to recognize that it nuclear propulsion's advantages are not all encompassing --- but also that the its more limited advantages for certain vessel types can still make it valuable to pursue.
In the case of the PLAN, the primary benefits of nuclear propulsion relate to reduced refuellling frequency needs compared to conventional carriers (as well as additional free volume for aviation fuel or other components), and overall logistical benefits to the taskforce.
When the biggest vessel doesn’t require refuelling for its own transit needs, it means you only need to refuel the carrier for its aviation fuel, which can mean the difference between needing additional replenishment ships for the task force. Meanwhile consumable dry stores can be done via vertrep or underway replenishment if needed (if one is expending munitions; food is somewhat more easy to anticipate).
Nuclear propulsion for a carrier as part of a task force that is otherwise conventional, doesn't obviate the need for a solid logistical support component, but it may significantly reduce the scale of it.
