I suppose you'd want to transition from ship to shore via a DC path and convert it back to synchronized AC which should avoid issues with reactive loads.
If the ship did have significant MWe capability you would have no way to get it shoreside, the shore power cables would burn. In availabilities where significant shore power is required (>800 Amps), sets of cables have to be welded directly to busbars because the sockets can't handle it.
So you've got 360kW (800A * 450V) that the average plant can deliver. The typical estimation is 10kW per home, so 36 homes from one naval plant.
> It is estimated that the total thermal power output of the A1B will be around 700 MW
CVN-78 has two of them.
> A1B reactors likely produce enough steam to generate 125 megawatts (168,000 hp) of electricity, plus 350,000 shaft horsepower (260 MW) to power the four propeller shafts.
When fuel lifetime becomes an issue for a nuclear naval vessel they will have propulsion limits in place that limit transit speeds to those which are most efficient for the propulsion turbines.
More often they use the onboard desalination plants (also nuclear powered) to make lots of fresh water.
e.g. https://www.militarynews.com/norfolk-navy-flagship/oceana/ne...
But building storage before you have enough renewables to charge it from would be stupid. So, the money goes to generating capacity, in the meantime. When storage is needed, it will be much cheaper than today, as cost is falling even faster than generating capacity.
[0]: https://energy.hawaii.gov/wp-content/uploads/2022/01/HSEO_20... ( pdf warning )