Here's my angle on it. I've been flying backwards and forwards round the world the last 3 years with my band. It seems to me that whether you can carry on or not does not depend generally on airline policy but the person at the checkin desk. I of course would prefer to carryon all the time but due to the uncertainty of getting a yes, I have decided to take the option that protects my instrument from damage which is to flight case it. I know that does not protect it from theft or getting delayed or getting diverted to another airport. Fortunately I have always arrived at the same place as my luggage.
Only one occasion when I took the guitar to the USA for a gig last year february I was refused permission to carry it on the plane back. That was when we flew back from Atlanta to London. The air staff refused to allow me on to the plane with the guitar in gig bag unless Paid for a seat. ( I had my alembic with me so you can see I was concerned)..
Even when I pointed out how stupid that rule was because if my guitar was on a seat and if the plane had heavy turbulence, the guitar may work its way out of the seat and hit someone. Far safer in the over head, and In that case would they indemnify me against any injury claims caused since the guitar would be carried under airline policy.... NO ANSWER.
Anyway in my experience I cannot take the risk of taking a guitar in a gigbag and find I can't take it on board so I always now take a flight case and check in to oversize baggage. My case has so far been damaged dropped from the baggage cart. saw it through the plane window, come back soaking wet. But the guitar has never been damaged.
In the UK the airlines and the Musicians Union worked out a deal where musicians travelling to professional gigs abroard are allowed to carry their instruments on board if it will fit into the overhead. Since that ruling came out last year I've still not had an airline give me a definitive YES.
Interestingly though when I've seen people carrying an acoustic guitar to the checking looking like they are going on holiday, they always seem to be allowed to take it on board. Maybe thats because it doesn't look like an electric guitar. So maybe you should get one of those guitar cases with feminine curves and they may allow you on.
Hope that helps.
As a light hearted extra, you do get to see a great x-ray of the guitar as it goes through the security machine., All the innards, the twin truss rods etc can be seen clearly. It's great. As yet I havent managed to persuade the staff to send me a photo.
Jazzyvee