Imagine a super large cruiser as large as a Nimitz-class supercarrier, armed with many types of advanced missiles and other types of weapons. How effective will such a ship be? If people didn't realize the effectiveness of aircraft carriers, battleships would probably continue to evolve. The Kirov-class cruiser is probably the closest thing to a modern battleship. It is as large as a battleship, but much lighter due to its lighter armor.
From the US Navy perspective, the closest thing to this, outside of the refitting of the actual Iowa class battleships in the 1980s, was the study done in the 1990s for the arsenal ship by the US Navy.
Let's talk briefly about both.
The Iowa class battleships were modernized and refitted and then used in modern combat. They were awesome ships for their entire service life. Their heavy guns were excellent for fire support, accurately firing a 2,000 lb projectile over twenty miles. Their heavy armor was even feared by the russians because they were not sure that modern torpedoes or the ASuM of the time would penetrate it.
As modernized, they were armed with 32 cruise missiles (a lot at the time) in armored box launchers (no longer capable of launching todays Tomohawks), 16 haproon missiles and four CIWS. For the 1980s this was a heavy Anti-surface and self defense armament. They were protected by other cruisers and destroyers for ASW and umbrella AAW coverage, being treated as very important capitol ships much like the carriers in that regard.
They were also fast and are one of the few ships that were capable of coming close to keeping up with a modern carrier if the carrier pulled at all the stops. The Burkes and Ticos cannot.
Because of their WW II construction, these vessels VERY man power intensive and simply too costly to continue to operate. So they were decommissioned again. Today, they would now cost more than than the full construction cost of a new Burke destroyer to modernize again. They were beautiful and they were used in combat throughout their careers, having actively served in WWII, the Korean War, the Vietnam War, off the coast of Lebannon, and in the first Gulf War against Iraq. As I said, all four were decommissioned again between 1990 and 1992.
Here's a picture of the USS Iowa firing a full broadside in 1984. Note the armored box launchers and the harpoon launchers. The second is of the USS New Jersey firing a boradside in 19984 as well, note the CIWS in that picture.
Now, the arsenal ship.
In the 1990s the US Navy investigated constructing a large vessel that would be armed with a very large number of VLS cells (up to 500) for crusie missile and anti-air work, as well as multiple, modernized guns (along the lines of what will ultimately be on the DDX using Excalibur like features) for long range fire support missions. They wanted to develop a modern day equivalent to a battleship for the role of providing fire support on shore, well beyond the range of what the conventional, older battleship had been able to do.
The Arsenal Ship was a joint US Navy and DARPA program at the time, meant to acquire very high firepower vessels, that were not terribly expensive, with as low a manpower requirement as possible. Four to Six ships were envisioned and were to be built for delivery starting in the 200-2001 time frame.
The design went through several phases with phase two contractors being selected which included Lockheed Martin, Ingalls Shipbuilding and Newport News Shipbuilding in 1996. But the program was cancelled in 1997 being judged redundant to the twenty first centruy surface combatant (SC-21) program which later produced the DD-21 program to produce up to 30 destroyers with similar capabilities (albeit smaller numbers of VLS cells and guns per ship).
In other words, the leadership, and probably understandably and appropriately so once the new plans for the smaller vessels began to mature, decided to do the same job with similar functions on smaller vessels and to build more of them.
Having said all of that, to this date however, the DD-21 (which had now evolved into the DDX progam) has not produced a single ship ten years later, and the overall numbers for that program have been reduced to 8-12 ships, not many more than the original Arsenal Ship plans.
Here's a picture of what the Arsenal Ship was depicted as looking like.