Well Colonel Shawn Welch isn't advocating for a BB(X), he keeps things simple within the scenarios I outlined above. His modern capital warship would be similar to the Iowa, not the DD(X). Thus much cheaper than my BB(X) concept. His thesis relies mostly on existing technology. He outlays several scenarios for mitigating the joint fires gap. However, building a modern capital warship with major caliber guns would be feasible with the elimination of the planned 12th CVN set to be laid down 2015-2019, and most cost effective.
Also, Colonel Welch outlines some of the long-range projectiles designed for 16" guns for the Iowa's, which are still viable for future research/production. One was a mass-fraction rocket based projectile designed in the 70's, which would have had a range in excess of 200 nm, and a Ram jet projectile, which had a feasible range of 400 nm.
The main problem here, is that you're actually comparing two different scenarios. It is true that a carrier and future battleship would be very different. However the difference is, is that we already have 11 carriers. However, we have no surface assets capable of mitigating the joint-fires gap. He's arguing for balance.
Debating a BB(X) is inherently different. Because the ship I outlined in the beginning of this thread is 2/3rd the price of a carrier, much more than the more simple capital warship that the Colonel outlines, and while it would easily mitigate the joint-fires gap, it fills a different role. It depends on what you're wanting to discuss as far as the BB(X) goes.
I originally conceived the BB(X) when the Chinese unveiled their DF-21D ballistic anti-ship missile. It's a medium range ballistic missile converted to a be armed with a kinetic kill warhead. Possibly with MIRV's, all armed with kinetic kill warheads. Currently the USN has stated that there may be no known defenses that could reliably defend against such a threat once it's in the terminal phase. (It's speed upon impact is in excess of Mach 10). They've also used another version of the same missile to shoot down a satellite in relatively high-earth orbit.
A BB(X) is designed with the idea that carriers may not be able to operate with the same amount of ease in combat zones as they did in the past. A BB(X) could have a relatively small RCS and the ability to operate with more viability in contested combat zones with an opponent that has similar weapons to the Chinese. With technologies like this, we have to assume that they can destroy a carrier as long as they can target it. This may lead to ASAT operations on both sides (to destroy spy satellites/GPS satellites capable of locating and targeting them). While a BB(X) wouldn't be invincible to radar by any means, it could have a much smaller RCS than a carrier, which has a giant flat flight deck to worry about.
The idea being, that a BB(X) could move in and hit ballistic missile locations, along with stealth aircraft in lieu of a carrier moving into range for more conventional strike missions. A BB(X) also would not be exposed to advanced SAM threats, while carrier aircraft would in the early stages of any type of opening strike. With the known missile locations hopefully knocked out, a carrier could enter into range more safely than otherwise. This of course assumes that the DF-21D is the only type of missile taken into consideration for such a scenario (it has a range of 3000 km). And of course it would also mitigate the joint-fires gap as well. Joy.
http://en.wikipedia.org/wiki/ASBM
Also, it's important to remember that a battleship with cruise missiles and UAV's can easily have a range of 1200-1700 miles. And can fill many of the missions a carrier can within that range. A carrier has a similar range, except when accounting for refueling. In order to understand the problems with the joint-fires gap, you'll have to read his thesis. It will explain everything to you very clearly regarding that problem.
Also, one BB(X) or one Capital Warship wouldn't be able to mitigate the joint-fires gap. Because one ship cannot be on station all year long. It has to take its crew back home at the end of their deployment, has to refuel/rearm, has to do any number of things that take it away from it's combat zone. Therefore you need around 3-4 ships to adequately fulfill the needs of the USMC and USN.