A critical thing with flying in on the day of the cruise is if you have to go through a hub. A direct flight from your airport to the cruise port makes things less stressful. But when you have two flights to get there, you have added a lot of potential problems.
I'll admit that despite my pleas to people to fly in a day early, I have done two cruises over the past 18 months where I ignored my advice. The last was just a month ago. Scheduled to leave Huntsville at 5:30am, change flights in Atlanta with plenty of time, and then get to Fort Lauderdale by 11am. Easy right? But then a computer problem hit the FAA flight planning system (just as it had done a week or so prior). We sat on the tarmac at Huntsville for about a half hour before the Captain announced we were lucky because our flight plan had made it into the system before the computer glitch. But we were still late and had another 20 minutes before we could leave. My whole cruise flashed before my eyes. I had insurance but still, I knew I might be in trouble if Atlanta was in chaos (highly likely at that point). We finally got to Atlanta and I had 20 minutes to get from one concourse to the other. I ended up being the LAST person to board the flight to FLL. Thankfully the computer problem was resolved and we were able to leave almost on time. So I got to the Oasis Of The Seas with not further problems. But I have to tell you, I told myself "never again".