I recently had a transatlantic cruise on the Prima, using the NCL air. My experience: Los Angeles to London Heathrow, via Rome. This flight was on ITA airlines, formerly Alitalia. We flew directly over London to Rome, had a two hour layover then on to London. I'm assuming it was cheaper than a direct flight. Baggage was free, typical 50 pound limit for the checked bag, one overhead bag, and an under seat bag. It was an economy class. I have no complaints other than the previously mentioned roundabout route. The cruise ended in New York, the flight was out of Newark, New Jersey. Baggage was also free, and economy class on Delta. The shuttle bus took us directly to the airport from the ship, but our flight wasn't until 8:30 pm. If I could have figured out what to do with our luggage, I would have skipped the shuttle, spent some time in New York, and taxied to the airport. As it was, we got to spend all day waiting at the airport. When we checked in, we had the option of going standby on one of three earlier flights, but we'd be taking a gamble. Why NCL chose the late flight, I'm guessing because it was cheaper. We landed in Los Angeles at 11:30 pm. I wasn't willing to chance of driving 35 miles home with a good chance of not staying awake, so we got a hotel.
We did take advantage of deviating the flight for two days prior to the cruise. This really meant only one day in London, as the first day was getting from the airport to the hotel, getting dinner and going to bed. We spent the next day in London, then the next getting to the port in Southampton. Two days is the maximum deviation NCL allows.
Not a horror story, but not the most convenient itinerary. On the plus side, the price for the two of us was $599, about a third of what I would have paid if I'd have booked myself. Then there was the added cost of the hotel at the end. Is it worth saving the money of the flight for the inconvenience? You'll have to decide for yourself.