"But if you book your air through the cruise line's premium air program they will make sure you get to the ship."
This is what you said and it is simply not true. The small print the cruise lines use is they will "work with you". No guarantees. Having a good TA, absolutely, they can work and try to rearrange things, but having a ticket without the restrictions of being assigned to another airline, is priceless. This I say from experience.
A lot of people are very comfortable letting the cruise line take care of the details and that's great. But please don't tell people that they will get you to the ship, as thats simply not true. The PVSA plays a big part of not being able to meet the ship if you miss the first port. You're better off having the airlines on your side to start with.