Nuke propulsion plants are expensive  , that's the main reason for their minimal use is smaller ships . That and they're heavy .

The US wasn't building any more battleships when nuke power became viable so that's why none were built .

Carriers are very likely to be engaged in combat  -- we're the number one target !

We had more than a few nuke cruisers that served for a very long time : https://en.wikipedia.org/wiki/Nuclear-powered_cruisers_of_the_United_States_Navy

Shock trials was definitely aimed at testing the integrity of reactor plant operation .

The control rods are held in place and moved in and out of the core by electric motors that have " claws " that engage the threaded shaft at the upper end of the control rod . The rods are continuously under spring pressure so when the claws are released the rods are slammed into the core via the force of the springs .( That's a " scram " . From , " Super Critical Reactor Axe Man ".

The first reactor utilized manually raised and lowered control rod that could be dropped by severing the rope used to lift it .)

They can't be shaken loose  , and the test proved it .

I trained on a one of a kind plant up in upstate NY  named  MARF , S7G .

It didn't use hafnium control rods but gadolinium tubes that controlled reactivity by controlling the height of the water within the tube .

It was a freak . I could go further into the core physics but it would require a lot of explaining .

That prototype is long gone . She was close to being spent when I was training on her back in 86- 87 .

I was looking over the Kesselring site using Google maps not long ago and the containment building is gone . No surprise .

It was probably decommissioned back in the early 90's , if it even made it that far .