I also have insurance for my instruments that covers airline damage and loss. When you fly on tiny commuter planes, you will have to relinquish your guitar, but you can watch the baggage person put it in the hold yourself, and at the end of the flight you pick it up right outside the plane, so it doesn't go through the maze of conveyor belts. I have never had a problem on these little flights. Don't push the airlines . If you are attempting to carry a guitar on board, don't bring a lot of other carry-ons.
Many people have to share limited space.
I have seen musicians carry on needless extra stuff and act indignant when they get called on it. A friendly positive attitude and gentle persistence will generally get you and your guitar taken care of in the best possible way. I always fill in the customer survey cards in the in-flight magazines and tell the airline that I am flying them because they have always been great about letting me on board with my guitar in a gig bag. Airlines cater heavily to business customers, and I remind them that we musicians are business customers, too. I always try to be friendly and polite, especially if I am carrying a guitar, so that airline workers will like accommodating musicians.