Why does everyone hate the Alaskas so much?
I sure many people find the Alaska class to be fine warships. They are sadly deluded, but I'm sure they are sincere. The Alaska class is, simply put, what happens when you give a military unlimited money and no one ever asks "Why are we doing this?" I will spare everyone one of my top line rants on the subject (in fact I think I may have laid one out in a thread you started a few weeks back) but if you search on my name and the ship class you will see much well deserved vitriol dispensed on the subject.
To your original question... The laughing stock is nearly impossible, even old WW II ships would be fronty line well into the 1960s (in fact were front line 25-30 years after commissioning IOTL). Turning the fleet into a poor relation however, that is quite easy.
Construct a POD that butterflies away the Korean War, or at least delays it into the 1960s. Prior to Korea that Air Force had managed to get about 3/4 of the way to convincing Congress (and more importantly, the electorate) that carriers, battleships, a large Army, etc. were a waste of money. All the country need was the USAF and bunch of nukes and everyone would play nice. Even after the Soviets joined the Nuclear Club the Air Force brass ( and a good part of the Pentagon and Armed Service committees) remained convinced that carrier task force was simply a big target and that a armored division was somewhat more diffused target.
What convinced people otherwise was USN (and RN with
HMS Trimuph) carrier launched airstrikes providing CAS that allowed ROK/U.S./UN forces to make it back to Pusan and then kept the Pusan Perimeter from collapsing along with tactical USAF assets. It suddenly dawned on folks that simply nuking anyone who looked crooked at the U.S., might not be the optimal solution.
I don’t know how an all nuclear navy is bad at all. It’s literally the wet dream of every country.
Not enough money in the world to support an all nuclear fleet of any size. It is, in some ways, similar to the problem Authur C Clarke described in
Superiority. You have the overwhelmingly better ship, but the enemy has 30 that are relative crap but cost 1/30th of your supership, and can be built in 1/3 the time. Then the war starts and all 30 of them come after you. You sink 15 of the enemy before your ship goes down. Your ship was obviously superior, but at the end of the day, who owns the water?