Fair enough. Currently each America-class ship [1] uses 2 GE LM2500 turbines [2]. This type of engine has been produced in huge quantities, more than 2000 to date. The unit cost is about $11 MM [3], so it's negligible compared to a naval nuclear reactor.
Where a nuclear reactor comes ahead is the fuel cost. Which is zero (it's included in the construction cost, and there's no refueling for the lifetime of the ship). A conventional turbine burns fuel, and over the lifetime of a ship it can add up to quite a lot. It can certainly get above $1BN.
In fact, the CBO analysis shows that the total cost for 5 such ships would be $14.2 BN using conventional engines, and $14.8 BN using nukes ([4] page 6 top table). That was when the oil price was $86/barrel. Now it's $110, so just because of that the calculus can switch to favor the nukes.