The Norwegian Cruise Lines website says the ship arrives at 8am and departs at 4pm, and that "Disembarkation usually begins 2 hours after docking. Due to security reasons, all guests must be on board 2 hours before sailing."

So it doesn't really seem like that much time on the ground in port. The website shows options for the Dolphin Encounter, an island tour, a trip to the Baths, and maybe snorkeling at Norman.

It actually doesn't seem so unmanageable to me. Some of the hundreds (thousands?) of guests are bound to spend a few bucks around the BVI, so that's a win for the islands.