I do know that most or all of our Navy ships are highly computer controlled/integrated, so maybe the following would be moot today, but...

...wouldn't it be prudent for officers to have the skills to plot and do things on paper in the event that during combat or for other reasons the ship sustains such damage that limits or eliminates the ability to use the computer systems to do that same task?

Again - maybe it's one of those things where if the computer systems are down in such a way that you can't do the task, it is likely that you have bigger problems to worry about. Even so, I would think this would be a critical skill to have, if a "just-in-case, cover-yer-butt" scenario presents itself where it could mean the difference between life or death, survival, rescue, etc.

Seems the best reason to teach these things isn't because we expect them to be used to any substantial extent in combat, but because they're critical and necessary exercises for honing and maintaining the skills needed to wield the high-tech tools, much like in bballard's example. Learning and regularly applying the fundamentals is often critical to understanding the problem space. When you're commanding a naval ship I imagine the problem space is immensely complex, much more so than most other roles in the military, or anywhere else for that matter. If you can't foresee or recognize the problems quickly, you certainly won't be able to respond in a timely manner no matter how fancy the tools.