you note that air launched missiles are limited in size for the USN without mentioning the huge increase in size, cost and complexity necessary to get a weapon to 30,000 feet and 500 mph from a ship.
That is true, but the ship has the means to support such large weapons, even with boosters. Thus range and payload are ultimately greater than any ballistic missile the Super Hornets could launch, which would have to sacrifice one or the other. CPS offers quite frankly tremendous range (stated to be larger than 2000 nmi) and a substantial warhead, while something like the Israeli Rampage has a very small warhead and much lower range, so it's usefulness and the usefulness of systems like it are questionable in a naval context, LORA is only marginally better. Even the massive Kinzhal, arguably the poster child of the modern ALBM and the one with the most extensive usage to date, doesn't boast such specifications. This obviously ignores the very fact that a weapon like Kinzhal or something of similar size, range and warhead couldn't be used on carrier launched F/A-18E/Fs. So you don't have an air launched ballistic missile for the Navy that could rival the ship launched CPS.
In general it's not like BBG(X) opting for CPS would be dentrimental in any shape or form. It doesn't mean that there will be subs without it as a consequence, in fact it increases commonality between the Virginia-Class, Zumwalt-Class and Trump-Class. So it should avoid the pitfalls of AGS in that regard. And having a ship that's able to defend itself, others and simultanously be able to shoot back or shoot at attackers that may not even have the range to retaliate, that's worth something. That also doesn't mean it's primarily a ship killer, that's a submarines job. But it has the capacity to dish out significant damage within a short time frame against high value targets over vast distances.
As for the general sentiment some shared regarding eggs and baskets, a CVN has near zero self defense capabilities, relies for offensive actions on tactical aircraft (which are certainly easier to engage and shoot down than ballistic missiles with hypersonic glide vehicles), ties up and relies completely on several high value surface combatants to protect it, is essentially a swimming city with tons upon tons of aviation fuel, bombs, aircraft, missiles, spares, rations and literal air traffic control on board, inhabited by God knows how many thousand people. You can't really put more eggs into a single basket than with a carrier, just that the carrier cannot defend itself, neither can it return fire, in fact it steals the eggs from the overarching big basket as it requires a substantial numbers of escorts. Now even if you want to use your BBGN not completely autonomously, but part of an action group, that would mean like one additional destroyer? Maybe a frigate and a submarine? Just that the BBGN can effectively contribute to AAW as well as
long range precision strikes. Now, that doesn't mean that it can or should replace aircraft carriers. An aircraft carrier can lay down a proper beating, especially against far less sophisticated adversaries. And something like an E-2D provides tremendous benefits to a wider naval force. But it's still a lot of eggs in one basket. Which is why I don't think that argument really works for the far more independent BBGN which ties up less resources.
