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I can all but guarantee that the logic was something like:

1. A nuclear powered ship can run at full power until the food and ammunition runs out.
2. Therefore a task group with nuclear powered ships must be able to sustain full power for some large number of days
3. Therefore the future destroyer must have enough fuel to run at full power for that period
4. Therefore the future destroyer must resemble an abnormally fast tanker with some missiles on top.

This kind of logic is usually used by someone with an axe to grind. In this case, most likely either 'the Navy needs nuclear destroyers!' or 'this is no way to run a fleet, look how ridiculous the destroyers are!'