Dumb idea : why not rechargeable electric warships? Design it so it can be recharged from a nuclear powered submarine docking to it underwater.
The goal is to have an entire taskforce of cheap BEV warships all supported by 1 or 2 expensive nuclear charger subs, giving the entire group effective infinite range at low cost. Plausible?
Energy Density
Batteries give about 0.5 MJ/kg
Diesel gives about 45 Mj/kg. Even at 20% conversion, we're still looking at 10~20 more range/endurance for a similar displacement given over to fuel vs battery.
Cost Savings
The bulk of a warship cost is in electronics and weaponry, not in the hull and propulsion.
That's why you have ideas of arsenal ship with CEC weapons as you have significant savings on not having to put sensors and CIC on the arsenal ships.
With battery and IEP tech, you will still end up with an equally expensive warship and an even more expensive AO/AOL sub.
Safety
Water and fuel is not a dangerous mix. Spillage of fuel during UNREP is not a major issue compared to water getting into the recharging harness during Electric-UNREP.
Also, runaway discharge caused by minor combat damage on such a big battery pack ... nightmare for ship damage control.
Benefits do not transfer
EVs benefit from energy recovery when the vehicle slows down - which is why EVs typically have better range in city as opposed to highway driving. Warships on the high seas do not benefit from this.
Non-Nuclear Submarines benefit from batteries as they typically use the silent mode for low speed, silent transit. Energy efficiency from batteries is linear so high speed transit (which increases the energy requirement significantly) will draw down a battery really quickly. Fuel and engine types can be matched to power requirements, which is why you have various forms of CODAG/COGAG to deal with the long constant patrol speeds and occasional burst of flank speeds.
Solution looking for a problem
A ship doesn't just survive on fuel, it needs other supplies as well.
If you have to have a platform alongside for UNREP, then why replenish from a submarine form factor when you can replenish from a AOL ship with similar deck heights and various cranes and stations to facilitate ship-to-ship transfer of dry supplies.
Those are what I came up with over 5 minutes of thinking it through.
What did you see as the benefits to start with?