Multiple crews allows you to keep the sailors rested, and ready for intense operations. One of the problems with ships operating continually, was that they suffered more wear and tear, and required more work from the crew to keep everything operational. In the past, ships would come back after a six month tour and spend a lot of time in port, where maintenance was done. New ships are going to have design features that can better handle the longer times at sea. But for older ships, like the Burke class destroyers, the large (320 sailors) crews were too complex for Sea Swap. That's because a lot of people on Burke class ships are cross trained for different systems, and not every Burke class ship has a crew with the exact same distribution of skills. Moreover, in the larger ships, the crew has more people away for training, leave to temporary duty. This creates gaps in your crew skill set that often does not match that of the crew you are relieving.
The concept of multiple crews is nothing new. Ballistic missile submarines have been doing it (using two crews to maximize the time the subs can stay at sea) for two generations. And the air wings (several thousand sailors and pilots strong each) that operate off carriers, have also been going from one carrier to another, with shore assignments in between, for many decades. Multiple crews were also used with the coastal patrol boats the navy built in the 1990s, and now uses in the Persian Gulf. The new LCS crews are designed for multiple crews. But for older ships like current classes of destroyers, Sea Swap created more problems than solutions.
The U.S. Navy is finding that its "Sea Swap" program (assigning several crews to one ship) doesn't work for ships of all sizes. The original idea behind Sea Swap was to eliminate the transit time, which can be up to a month, as the warship makes its way out to a far away area (like the Persian Gulf), for a six month tour. With Sea Swap, the ship stays out there for 18-24 months, while the crews do their usual six months at sea before flying home. Thus these ships can stay at sea constantly, without wearing out the crews. This would mean that, for interdiction operations, where suspicious ships are boarded and searched, you can wear the crews out real quick, without putting a lot of stress on the ships.