What are you smoking man, cause I want some of it...
My fellow Alembican, the nature of traveling with a very delicate instrument, is completely acknowledged and very well understood by most commercial airlines.
Surly a private business has the right to allow what ever they deem, and to serve who they wish, but one thing you failed to understand and support is: TSA does control what can, and what passingers can-not board on airlines. No Airline can allow you to board a plane items that are banned. (A moot-point)
The definition of cargo (Musical Instruments) had already been written, and signed off with TSA.
Thus under those guidelines, warrents protocol as such, to honor passengers with musical instuments and one carry-on.
Sure, it's wise to call your airline first, (that's completely prudent) but believe me, there are musical institutions all over the world who'd had lobbied strongly so that we may feel at ease about this concern.
I know my rights.
The strongest point on this topic, is:
The size and remaing overhead lockers availble for your guitar.
However, if there's no room available, then out of safety reasons, Airline personnel would have and in some situations, must use descretion with any bag....
Therefore it pays to reserve an early flight or take flights that are least likely to be full.