As mentioned by butler180, it’s the ultimate “learning the ropes” team-building exercise. If the guy I spoke with on the Spanish training ship Elcano is to be believed, that crew often does no-lifeline drills up in the rigging (as in, let go and you splat 40 feet down onto the deck or 50 feet into the drink), which I’m sure really focuses their attention.
Like Little Nemo mentions, land forces still do rank-and-file formation close-order drill, which are the tactics of the age of pikemen and musketeers, so that they may develop the mentality to function as a unit.
Not only that but it the sailing school-ship also gives the midshipmen valuable experience doing physical grunt-work AND getting a “feel for the sea”, being able to asess conditions w/o constantly looking at the computer and, this is quite important, developing a sense of respect for what the elements can do. Mostly officer candidates get this training because they will be the ones responsible for steaming theiir crew into a bad situation. On a sailboat, getting out of trouble is even harder than on a powerboat, you can’t even shout “Full Reverse!” and hope it works before you hit the rock.
Besides, sailing into a port-of-call on a Tall Ship rather than some squat grey retired minesweeper probably means half your local-babe-pickup work is done before you lower the gangplank 
In the USA, the academy that uses a Tall Ship is the Coast Guard’s, not the Navy’s. And I see where it makes a lot of sense since they will have to deal a lot with interventions (rescues, seizures, inspections) on sail vessels, AND be called on to go out in foul weather.
I think you mean a sextant. But yeah, someone should be able to get the boat safely into the harbor if the computer bluescreens.
