Disney recommends nothing before 12:30. I suspect they make that recommendation based on their experience with things that frequently go wrong.
We had a 12:35 pm flight and made it, but with only 20 minutes to spare.
We had late seating breakfast, so ate and were in line to get off the ship at 8:30. The wait was 45 minutes to get off the ship. It took 15 minutes to get our bags, clear customs, check our bags with the airline at the port, get on the bus, and be on our way. We left the port at 9:30, and arrived at the airport at 10:15.
The big problem was a 90 minute wait to clear security at the airport. We arrived at our gate just 20 minutes before boarding. I prefer to be there an hour before.
So yes, some do make earlier flights, but THERE IS A REASON Disney recommends nothing before 12:30.