I have flown with rifles to Africa, Alaska, Phoenix, Australia and a few other destinations, without incident.
Flying to Phoenix was the most interesting and having done it several time, somewhat the most nerve wracking. For a long while, they had the worst luggage theft rates in the country. Part of this was because they never checked luggage tags against the ticket tags that are issued at the same time. Another reason was that there was an elderly couple that had luggage theft for a hobby. For years, they stole luggage from the airport and filled up multiple storage units with it. Never opening or attempting to sell the stuff. Anyway, they were eventually caught.
But the best part of one of my Phoenix trips is that I saw every loading and unloading of my flights - 2 each way and was able to see my gun case handled each time. It was fascinating to watch the handlers pitching case after case of golf clubs into carts from conveyors and from conveyors to carts. It was like the Olympics of golf club tossing. Denver was the intermediate airport and all three were the same with regards to how they handled clubs. But every time my case took its turn, someone would walk up, grab the handle with both hands and carry it to wherever it needed to be and gently put it down, ensuring that it was straight secure. It was amazing. Not sure why. It did weigh right at the max of 50 lbs. Gun case tossing is not an airport sport apparently. But golf cases --- that's another story. And I know some guys like to "disguise" their guns in golf cases. Not me, not after that.