An unarmed Aircraft Carrier can be used for anything. Much like a Starship can be used for anything. The fact that it is unarmed just allows the hand to be presented open. The airplanes can be carried or not. Any gester can be made depending on what you put on the carrier. The same for Starfleet. It depends what you put onboard that counts. Never go overzealous in attributing military hardward to Starfleet. It does not suit them.
As for Japanese carriers in World War II. Kaga and Akagi still had some of their 8 inch guns mounts on the sides of the ships. They had had twin turrets like the Lexingtons prior to their 1930s refits, but those were removed as they took up space needed for the new decks. Also the likely wouldn't ever get in range to use them in combat anyway. The Lexingtons had their 8 inch turrets removed in 1942.
Mind you that the USS Enterprise (NCC-1701) was likely named for the World War II carrier, not the, at that time, new nuclear carrier. I say this since it had been the idea to name the ship USS Yorktown, Enterprise's sister ship and the class ship of the Yorktown-class carriers. She was the star right up to her sinking. Enterprise probably never made it to the legend of Yorktown during the war, she was a tough ship that kept going, but Enterprise was by far more legendary as the survivor who saw the most battles.
I'm aware of the fact there was the USS Enterprise CV-6 and the USS Enterprise CVN-65 and I have an actual piece of the flight deck of the former in my office as my most prized World War II possession
Actually the Enterprise CV-6 was by FAR the most famous US carrier of WWII, way more than the CV-5 Yorktown. The Yorktown herself was in two major battles (Coral Sea and Midway) before she was sunk. The Enterprise participated in every major battle except Coral Sea and one other I can't remember off hand and she only missed Coral Sea because she was the escort carrier for the Hornet on the Doolittle Raid. She was also the ship whose aircraft bagged 3 of the 4 carriers sunk (Yorktown's got the other before she was sunk) at Midway, the most decisive naval engagement of the whole war.
She won 20 Battle Stars, the most of any ship in US history and did it in a span of 4 years. Ships have had 40-50 year careers and none have matched that total. No other carrier was even close. She was the only ship in World War II that won the Presidential Unit Citation and the Navy Unit Citation and is the ONLY non British ship in history that has been awarded and Admirality Pennant by the Royal Navy. And it's one of the biggest disgraces in US history that she was sold for scrap. It's like if they built a strip mall and condos on Gettysburg.
The only other two US ships in WWII that could claim to be as famous were the Arizona and the Missouri. One's claim to fame was how many people were killed in it's destruction and had no WWII combat career and the Missouri had a very short and undistinguished combat but happened to be named for Harry Truman's home state and was selected, over far more other worthy ships, to be the site of the Japanese surrender.
I have no doubt the WWII Enterprise was a large part of why the name was chosen, but it didn't hurt that the most famous active ship in the Navy, as well as generally to be considered the most powerful surface ship afloat at the time TOS premiered was also named Enterprise. A ship that was also a pioneer for being the first nuclear powered carrier.
As for your, the ship can be an ambassador too, I agree. But almost any weapon can be used for other purposed. B-52's can be unloaded and used to transport people if necessary, other Navy ships are often used as rescue vessels, the Blue Angels and Thunderbirds carry no loaded weapons during their shows of goodwill, an AK 47 could be made into a lamp....This doesn't mean at their core they're still weapons designed to kill and destroy things.
The ST Enterprises were, at their core, ships of war. I don't care how many goodwill missions they went on or the fact that in TNG families lived on the ships. They were vessels that were HEAVILY armed with weapons for defensive and offensive purposes.
There may have been other starships that carried little or no firepower and weren't really warships, but the Enterprise of any letter was always a heavily armed first line ship of war and it's clear those systems, besides the warp system, were usually the most important ones in the ship.