You are partly right porch but your post should read Qantas and the rest. Because only Qantas have the amount of flights/capacity to get you to your destination in time for most appointments.
I got caught out a year or so ago with
VB going to Syd from ADL to join a cruise leaving at 5pm. My flight left at( or supposed to) about 9.30am but due to technical difficulties (no cabin crew) it didn't. The next flight was about 12.30pm and was full the next after that got to Syd about 5pm so useless to about 10 of us. Luckily for us that amongst us was a travel agent that had connections somewhere because she managed to get 10 passengers bumped off the 12.30 flight so we could make the ship. When we flew out at 12.30 the 9.30 flight was still sitting there so I don't know when they finally got to Sydney. Qantas meantime had flights to Sydney about every hour so if it had happened to them they would still have got us there in time no drama. I learnt a valuable lesson that day. If you MUST get somewhere on a given day pay the extra and go Qantas or go a day before and blow any savings on accomadation. For any other cases however where it doesn't really matter if you are late go Tiger etc and enjoy the savings.