...SWOs are ship drivers and fighters...or at least, they're supposed to be. You should at least be able to drive the damn ship competently. And yes, to the point where the Captain can hand off conning alongside to one of the DHs and JOs and he should just sit in his chair, being captain-y.
Then send them to their first ship for 12-18 months and don't give them any divvo duties. Their focus should be on qualifications and learning what's what around the boat. Assign them to a second-tour divvo as a running mate/mentor/whatever. It's a probationary period...at the end of that 12-18 months, they should be fully qualified and pinned, or let go with a non-attain. Then they roll to another boat for a 24-month tour and then and only then do they really need to start worrying about Divvo bullshit. I really would like to see the community shift their focus from being bureaucrats afloat to professional, tactically-minded mariners.
In another thread about this very subject some time ago I referenced an article from Proceedings written by a LT who had done a PEP tour with the Royal Navy and from his description the Brits do much of that already. I don't know what their initial training is but they did do a stint on a ship where they primarily learned shiphandling, I think for 6-8 months, and then went on to another ship to learn Navy stuff. They also had to pass an international test/standard for shiphandling. I believe the Brits also split their deck and engineering officers as well.
Of course they also send their aviators on no kidding SWO tours and their carrier CO's don't have to be aviators so it isn't all roses with them!