The key point of having nuclear power is NOT just operating range. It is also endurance at speed and rapid deployment.
For example, if Chinese carrier fleets need to sortie to the Arabian Sea which is an integral part of the trade route between Pakistan and Europe - they would have to sail through the Straits of Malacca and around India to get there. Distance-wise it isn't far, Hainan to Pakistan is probably a shorter voyage than from Shanghai to Hawaii - only 3,500 nm compared to 4,500 to Hawaii, or 5,700 nm to go across the entire Pacific.
With a conventional carrier cruising at 16 knots, you can make the 3,500 nm journey from Hainan to Pakistan in 9 days. You can't afford to go much faster unless you want to burn all of your fuel. Sure you can bring a supply ship like the 901 and cruise at 23 knots without having to worry about fuel, but then that one replenishment vessel would become your lifeline. And at 23 knots, the journey would still take over 6 days.
But with a CVN, you can forget about all the constraints like cruising speed and fuel replenishment and keeping a big, defenseless fleet oiler afloat. The moment something bad happens, your carrier can set off from Hainan and sprint the 3,500 nm journey to Pakistan in just over 4 days at 32 knots non-stop.
The US went nuclear for not just the long-term endurance, but also the short-term endurance. If a crisis emerged in Europe while US carriers were stationed on the East Coast, they could make the sprint across the Atlantic into the Mediterranean in just 4 days. With a conventional carrier, it would take 2 to 5 days longer depending on your available supporting resources - an eternity if an enemy has already mobilized.