I agree, if that's what would happen, then your saxophone would stand a better chance of surviving. But when travelling recently, I was appalled to look at that rolling ladder contraption where the gate checked items descend from the plane, and see that it was equipped with a chute. Baby strollers and other easily carried items go down the way you describe. If I had gate checked my bari in its original case, it might have gone the way you describe.I GATE-CHECK the horn - this is the key. This means I carry it through security - it fits through the X-ray machine - and carry it to the door of the plane and leave it where the baby strollers go - it gets a pink gate-check tag at either check-in or at the gate - depending on the airline.. It is hand-carried to a separate luggage chamber & at the end of the flight, it gets hand-carried back up to the door of the plane.
When my case came back up to the plane, the SKB case had been subjected to some kind of impact that sheared off a latch and bent the valance open on one end. My bari was of course unplayable pending extensive repair. I don't think I would recommend gate check, because you'll go down the chute (if you're lucky - did mine make it to the end of the chute, or fall off midway down?) Nor would I recommend the SKB case: it didn't fit well, it was of cheap Chinese manufacture, and doesn't look to me like it provides the key support to the upper body. I have a '50s King, probably the worst case for fit, and I really don't have a good idea how a case could totally support a bari as required, but I don't think this is it. It's relatively light and cheap, though.