The Navy system would get energy from the carrier’s nuclear reactors for making jet fuel. While more expensive than Jet-A, the cost differential shrinks when eliminating underway logistical requirement (either eliminating the AOE or more space on the AOE for munitions).
Jet fuel is a bit lighter distillate compared to diesel.
I like the Navy’s approach and yes they have the nuke power plants afloat to make a refueling ship possible using seawater as feed stock.
Love my military scientists.