To be fair, she's DDG-151. Obviously the timeline is screwed up, but we're only up to around DDG-115 in the water, and FLT IIA ends at 125 (with a screwy one-off mixed in after). Nathan James would be a late FLT III or IIIA, maybe they regretted the lack of torpedo tubes and added them back into the design in case they were the last surviving Navy vessel and had to fight subs and battleships for some reason?
Edit: looked it up, it was apparently DDG-80 in the book and they didn't want it confused with a real ship so they picked a number high enough that it would last a while. For funsies, the Roosevelt (DDG-80) is homeported in Mayport FL, where they based this season, so may have even been available. And it's a FLT IIA.
Also, this may hold up longer than Last Resort, which picked Colorado as their Ohio-class sub. Name was almost immediately in use for a Virginia Class sub, may have even announced the name before the series was finished. In their defense, they picked the right naming convention and grabbed a state that hadn't been used yet, just went bad immediately...